From MAILER-DAEMON Thu Dec 28 16:48:03 2006 Date: 28 Dec 2006 16:48:03 -0400 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1167338883@mta.ca> X-IMAP: 1157207233 0000000028 Status: RO This text is part of the internal format of your mail folder, and is not a real message. It is created automatically by the mail system software. If deleted, important folder data will be lost, and it will be re-created with the data reset to initial values. From rrosebru@mta.ca Sat Sep 2 11:13:40 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 02 Sep 2006 11:13:40 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GJW5f-0002S9-P0 for categories-list@mta.ca; Sat, 02 Sep 2006 11:03:19 -0300 To: categories@mta.ca Subject: categories: no membership-respecting morphisms From: Paul Taylor Date: Sat, 02 Sep 2006 14:17:07 +0100 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 1 Mike Barr quoted a "thought of Chairman Pratt" that was attributed to him, > Monotone functions respect order, group homomorphisms respect the > group operation, linear transformations respect linear combinations, > and gangsters respect membership in the Cosa Nostra, but what > morphism has ever respected membership in a set? It is sheer hubris > for a relation that can't get no respect to claim to support all of > mathematics. (Old argument of category theorist Mike Barr, new > polemics.) and commented on it, > That is not a bad rendition (save for the reference to Cosa Nostra) > of what I actually said which was that we create these elaborate > structures of well-founded trees subject to the rule that two > chidren of the same leaf cannot be isomorphic. But then, unlike all > other structures that we build, we make no hypothesis that functions > preserve the structure. Indeed, I think a structure-preserving map > must be the inclusion of a subset. And there are no non-identity > endomorphisms. Of course, I entirely agree with the sentiment that epsilon-structures are completely inappropriate as a basis of most ordinary mathematics. However, mathematics and mathematicians are contrAry beasts, who treat any statement of the form "there is no such thing as ..." as a challenge, whether it be about membership-preserving functions or the square root of -1. Indeed, it's quite interesting to look at "carriers equipped with membership relations" in the same way as "carries equipped with group multiplications". This is what I did in my paper "Intuitionistic Sets and Ordinals", JSL 61 (1996). For a more categorical treatment, we may regard the relation as a coalgebra structure for the full covariant powerset functor. This is what Gerhard Osius did in his "Categorical Set Theory" in JPAA 4 (1974) and what I did for other functors in my unpublished paper "Towards a Uniform Treatment of Induction - the General Recusion Theorem" in 1995-6. (This was presented at "Category Theory 1995" in Cambridge and part of it appeared in Section 6.3 of my book.) As Mike Barr says, and Gerhard Osius proved in his paper, for "extensional" structures ("well-founded trees subject to the rule that two > chidren of the same leaf cannot be isomorphic"), the structure-preserving map must be a subset inclusion. However, without extensionality, it is a COALGEBRA HOMOMORPHISM. Well founded coalgebras behave like fragments of the initial algebra (the von Neumann hierarchy, in the case of the powerset functor), so their rigidity (lack of endomorphisms) is related to the uniqueness of homorphisms out of the initial algebra. The sense in which coalgebra homomorphisms are like partial algebra homomorphisms is explored in the early sections of my unpublished paper. Osius's recursion scheme has attracted some attention in recent years amongst functional programmers as a way of describing recursive programs. See "Recursive Coalgebras from Comonads" by Venanzio Capretta, Tarmo Uustalu and Varmo Vene, in "Information and Computation" 2006. In fact, the description also works for imperative programs - see Section 2.5 of my book. I have a longer survey of this subject that I intend to publish on "categories" later this month. MY WEB PAGES AT www.cs.man.ac.uk/~pt While I'm here, I'd like to draw your attention to some new things that I have put on my web pages recently. * The slides that I have used at recent conferences and seminars. * The unpublished paper and scanned transparencies of 1995-6 talks on well founded coalgebras. * A new web page for my book, "Practical Foundations of Mathematics", including where to buy it, errata, who has used or cited it, etc. If you have used it in a lecture or seminar series, please send me a URL and your experiences. * The full text of Jean-Yves Girard's "Proofs and Types". * A new version of my TeX package for "commutative diagrams", together with an explanation of the "PostScript" mode, why the "pure DVI" mode is strongly deprecated (NB those long-standing users who have spoiled their otherwise excellent books, papers and online journals by using it), and how to overcome its uglier features if you really insist on using it. * A collection of other TeX macros. * Scanned manuscripts of my 1983 Cambridge Part III Essay (= MSc thesis) (see "domain theory") and undergraduate algebra lecture notes. Paul Taylor From rrosebru@mta.ca Sun Sep 3 12:49:41 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 03 Sep 2006 12:49:41 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GJu1a-0001rE-1Z for categories-list@mta.ca; Sun, 03 Sep 2006 12:36:42 -0300 Date: Sun, 03 Sep 2006 05:26:44 -0400 From: "Fred E.J. Linton" To: "Categories list" Subject: categories: Re: Linear--structure or property? Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 2 George Janelidze and others answer affirmatively the question > Could you have two (semi)ring structures on the same set = > with the same associative multiplication? (attributed to Mike Barr) without ever noticing that the related question, of having two (semi)ring structures = on the same set, with the same addition, also has answer YES. For instance, take the additive group of 2x2 matrices with integer entries (or entries from any semiring) and notice that, apart from the usual matrix multiplication, there is also the sophomoric, or pointwise, multiplication (so called since it is generally only sophomores in the first week of their first linear algebra course who, following the analogous pointwise definition of matrix addition, would wish to multiply = two matrices by multiplying their corresponding entries). Not quite sure though how this impacts the situation with more than one object. -- Fred ------ Original Message ------ Received: Fri, 11 Aug 2006 01:06:56 PM EDT From: "George Janelidze" To: "Categories list" Subject: categories: Re: Linear--structure or property? > Dear Steve, > = > It is true that constructing such examples with more than one object is= ... From rrosebru@mta.ca Sun Sep 3 12:49:42 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 03 Sep 2006 12:49:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GJu0M-0001oK-B1 for categories-list@mta.ca; Sun, 03 Sep 2006 12:35:26 -0300 Date: Sat, 02 Sep 2006 17:54:37 +0100 From: "V. Schmitt" To: categories@mta.ca Subject: categories: Re: no membership-respecting morphisms Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 3 Paul Taylor wrote: >Mike Barr quoted a "thought of Chairman Pratt" that was attributed to him, > > > >>Monotone functions respect order, group homomorphisms respect the >>group operation, linear transformations respect linear combinations, >>and gangsters respect membership in the Cosa Nostra, but what >>morphism has ever respected membership in a set? It is sheer hubris >>for a relation that can't get no respect to claim to support all of >>mathematics. (Old argument of category theorist Mike Barr, new >>polemics.) >> >> > >and commented on it, > > > >>That is not a bad rendition (save for the reference to Cosa Nostra) >>of what I actually said which was that we create these elaborate >>structures of well-founded trees subject to the rule that two >>chidren of the same leaf cannot be isomorphic. But then, unlike all >>other structures that we build, we make no hypothesis that functions >>preserve the structure. Indeed, I think a structure-preserving map >>must be the inclusion of a subset. And there are no non-identity >>endomorphisms. >> >> > > >Of course, I entirely agree with the sentiment that epsilon-structures >are completely inappropriate as a basis of most ordinary mathematics. > >However, mathematics and mathematicians are contrAry beasts, who >treat any statement of the form "there is no such thing as ..." as a >challenge, whether it be about membership-preserving functions or the >square root of -1. > >Indeed, it's quite interesting to look at "carriers equipped with >membership relations" in the same way as "carries equipped with group >multiplications". This is what I did in my paper "Intuitionistic >Sets and Ordinals", JSL 61 (1996). > >For a more categorical treatment, we may regard the relation as a >coalgebra structure for the full covariant powerset functor. This is >what Gerhard Osius did in his "Categorical Set Theory" in JPAA 4 >(1974) and what I did for other functors in my unpublished paper >"Towards a Uniform Treatment of Induction - the General Recusion >Theorem" in 1995-6. (This was presented at "Category Theory 1995" >in Cambridge and part of it appeared in Section 6.3 of my book.) > >As Mike Barr says, and Gerhard Osius proved in his paper, for >"extensional" structures ("well-founded trees subject to the rule that >two > chidren of the same leaf cannot be isomorphic"), the >structure-preserving map must be a subset inclusion. > >However, without extensionality, it is a COALGEBRA HOMOMORPHISM. > >Well founded coalgebras behave like fragments of the initial algebra >(the von Neumann hierarchy, in the case of the powerset functor), so >their rigidity (lack of endomorphisms) is related to the uniqueness of >homorphisms out of the initial algebra. The sense in which coalgebra >homomorphisms are like partial algebra homomorphisms is explored in >the early sections of my unpublished paper. > >Osius's recursion scheme has attracted some attention in recent years >amongst functional programmers as a way of describing recursive >programs. See "Recursive Coalgebras from Comonads" by Venanzio >Capretta, Tarmo Uustalu and Varmo Vene, in "Information and >Computation" 2006. In fact, the description also works for >imperative programs - see Section 2.5 of my book. > >I have a longer survey of this subject that I intend to publish on >"categories" later this month. > > >MY WEB PAGES AT www.cs.man.ac.uk/~pt > >While I'm here, I'd like to draw your attention to some new things >that I have put on my web pages recently. > > * The slides that I have used at recent conferences and seminars. > > * The unpublished paper and scanned transparencies of 1995-6 talks > on well founded coalgebras. > > * A new web page for my book, "Practical Foundations of Mathematics", > including where to buy it, errata, who has used or cited it, etc. > If you have used it in a lecture or seminar series, please send > me a URL and your experiences. > > * The full text of Jean-Yves Girard's "Proofs and Types". > > * A new version of my TeX package for "commutative diagrams", together > with an explanation of the "PostScript" mode, why the "pure DVI" > mode is strongly deprecated (NB those long-standing users who have > spoiled their otherwise excellent books, papers and online journals > by using it), and how to overcome its uglier features if you really > insist on using it. > > * A collection of other TeX macros. > > * Scanned manuscripts of my 1983 Cambridge Part III Essay (= MSc thesis) > (see "domain theory") and undergraduate algebra lecture notes. > > >Paul Taylor > > > > Dear Paul, as far as i remember model theorists have an extremely elegant way of comparing structures: no morphisms there but "games" of finite isomorphism extensions (see Fraisse' and Ehrenfeucht for the game aspect or B.Poizat's book) All the first order syntax is subsumed by those games. I quite like categories and for sure I do not know everything, but I have not seen so far a convincing categorical counterpart for these games. (And model theory is good stuff!) Best, Vincent. From rrosebru@mta.ca Sun Sep 3 20:56:19 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 03 Sep 2006 20:56:19 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GK1lG-00077h-8j for categories-list@mta.ca; Sun, 03 Sep 2006 20:52:22 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: Book: Singular Coverings of Toposes Date: Sun, 03 Sep 2006 12:15:43 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 4 Dear categorists, You may now preorder our book (Marta Bunge and Jonathon Funk, Singular Coverings of Toposes, LNM 1890, Springer, September 2006) from amazon.com http://www.amazon.com/Singular-Coverings-Toposes-Lecture-Mathematics/dp/3540363599/sr=8-1/qid=1157299670/ref=sr_1_1/104-6910249-0361515?ie=UTF8&s=books Best wishes, Marta Bunge ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 Office: (514) 398-3810 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/bunge/ ************************************************ From rrosebru@mta.ca Sun Sep 3 20:56:19 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 03 Sep 2006 20:56:19 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GK1oL-0007Dm-UA for categories-list@mta.ca; Sun, 03 Sep 2006 20:55:33 -0300 Date: Sun, 03 Sep 2006 11:59:54 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: no membership-respecting morphisms Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 My request for precursors to Mike Barr's deprecation of set membership seems to have set loose a thread that has veered off from set theory into model theory. The following extract from the introduction to Gerald Sacks' "Saturated Model Theory" (335 pages, W.A. Benjamin, 1972) serendipitously ties up this loose thread while at the same time promising that category theory offers deeper insight into categoricity, a central notion of model theory, than the alternatives. "It is true that model theory bears a disheartening resemblance to set theory, a fascinating branch of mathematics with little to say about fundamental logical questions, and in particular to the arithmetic of cardinals and ordinals. But the resemblance is more of manners than of ideas, because the central notions of model theory are absolute, and absoluteness, unlike cardinality, is a logical concept. That is why model theory does not founder on that rock of undecidability, the generalized continuum hypothesis, and why the Los conjecture is decidable: A theory T is k-categorical if all models of T of cardinality k are isomorphic. Los conjectured and Morley proved (Theorem 37.4) that if a countable theory is k-categorical for some uncountable k, then it is k-categorical for every uncountable k. The property 'T is k-categorical for every uncountable k' is of course an absolute property of T. The notion of rank of 1-types was invented by Morley to prove Los's conjecture. There are proofs of it that make no mention of rank, but they leave one ill-prepared to prove Shelah's uniqueness theorem (Section 36). I have made rank a central idea of the book, because it is the central idea of current model theory. ... Morley's notion of rank was inspired by the Bendixson differentiation of a closed subset of a compact Hausdorff space; however, the Morley derivative differs from the Cantor-Bendixson derivative in that the former commutes with the inverse limit operation. The Morley derivative is expounded in section 29 as a transformation which acts on functors of a class common in model theory. One advantage of a category theoretic treatment of Morley rank is that it applies equally well to other notions [Shelah] of rank of 1-types. Section 25 reviews the apparatus of category theory needed in section 29." The difference between this recommendation of category theory for model theory and (for example) the literature on accessible categories is that Sacks was not a card-carrying category theorist but a recursion theorist. While category theory has no bias towards Goedel's notion of absoluteness (that I'm aware of), it seems reasonable to infer from Sacks' acceptance of CT that neither is CT biased away from absoluteness but rather is a neutral general-purpose tool. Vaughan Pratt V. Schmitt wrote: > Dear Paul, as far as i remember model theorists have > an extremely elegant way of comparing structures: > no morphisms there but "games" of finite isomorphism > extensions (see Fraisse' and Ehrenfeucht for the game > aspect or B.Poizat's book) > All the first order syntax is subsumed by those games. > I quite like categories and for sure I do not know everything, > but I have not seen so far a convincing categorical counterpart > for these games. > (And model theory is good stuff!) > > Best, > Vincent. From rrosebru@mta.ca Sun Sep 3 20:59:37 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 03 Sep 2006 20:59:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GK1s1-0007NW-43 for categories-list@mta.ca; Sun, 03 Sep 2006 20:59:21 -0300 From: "David Ellerman" To: Subject: categories: Re: Linear--structure or property? Date: Sun, 3 Sep 2006 11:32:20 -0700 MIME-Version: 1.0 Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 When a Boolean algebra B is treated as a Boolean ring in the usual manner, the meet is the multiplication. In his little-known thesis, Herbrand noted that a BA could also be construed as a ring with the join as the multiplication (see Church's tome on logic). Gian-Carlo Rota noted that both these Boolean rings were "opposite" quotients of what he called a "valuation ring" V(B,Z_2) which carries *both* multiplications and one addition. What is usually called "Boolean duality" (e.g., DeMorgan's law) is an anti-isomorphism of the valuation ring that swaps the two multiplications and leaves addition the same. The "trick" in constructing such rings was to see that the bottom element z (representing the null set) should be a separate element than the 0 of the ring. The usual Boolean ring constructed from a BA is really the quotient of the valuation ring that identifies z and 0, i.e., V(B,Z_2)/(z). The Boolean ring noted by Herbrand is the quotient of the valuation ring that identifies the element representing the top u with 0, i.e., V(B,Z_2)/(u). Remarkably, the valuation ring construction V(L,A) works for any distributive lattice L and any commutative ring A, not just a BA B and Z_2 and the anti-isomorphism works just as well. Thus we have "Boolean duality" over arbitrary commutative rings A; it has nothing to do with 0-1 nature of Z_2. This general theory of Boolean duality was developed in a series of papers by Geissinger in Arch. Math. 1973. See Rota's book "Finite Operator Calculus" for material on valuation rings. For the opposite question of two additions and one multiplication in a semi-ring, the natural setting is the algebraic treatment of series addition a+b and parallel addition a:b = 1/((1/a)+(1/b)) (e.g., from electrical circuit theory) in what might be called a "series-parallel algebra." Every commutative group G (written multiplicatively) generates a series-parallel division algebra SP(G) (think of all series-parallel circuits of resistors that could be generated with the elements of G as the resistors). It is a "division algebra" in the sense that the SP algebra is also a multiplicative group where the inverse of any SP circuit is obtained by taking the series-parallel conjugate circuit (see any circuit theory book) with the atomic resistances from G replaced by their inverses in G. Then "taking reciprocals" is the anti-isomorphism of the SP algebra that swaps the two additions leaving multiplication the same, and it algebraically captures series-parallel duality just as the anti-isomorphisms of the valuation rings captured Boolean duality. The SP algebra SP({1}) of the trivial group is just the positive rationals Q^+ (i.e., any rational resistance can be obtained as a series-parallel circuit with unit resistances) and the anti-isomorphism that swaps the two additions is just "taking the reciprocal" r-->1/r. There is an 1892 paper by the great combinatorist Percy MacMahon published in "The Electrician" that explains the notion of a conjugate of a series-parallel circuit and shows that if each resistence is 1 (i.e., G = {1}) and the compound resistance of an SP circuit is R, then the resistance of the conjugate SP circuit is 1/R (in case your library does not carry "The Electrician" from 1892, see the Collected Papers of MacMahon). Paying attention to the duality of series and parallel addition on the positive rationals or reals gives some cute dualities. For instance, instead of saying that the geometric series 1+x+x^2+... converges to 1/(1-x) for any positive x<1, it is easier to say that 1+(1:x)+(1:x)^2+... converges to 1+x for any positive x. And dually, the parallel sum infinte series 1:(1+x):(1+x)^2:... converges to 1:x for any positive x. Both Rota's valuation rings and the series-parallel algebras are explained in two chapters of my book: "Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics" (Rowman-Littlefield, 1995). Cheers, David __________________ David Ellerman Visiting Scholar University of California at Riverside Email: david@ellerman.org Webpage: www.ellerman.org View my research on my SSRN Author page: http://ssrn.com/author=294049 Now out in paperback: Helping People Help Themselves: From the World Bank to an Alternative Philosophy of Development Assistance. University of Michigan Press. 2006. For more information, see my website: www.ellerman.org . Book available at better booksellers online. -----Original Message----- From: cat-dist@mta.ca [mailto:cat-dist@mta.ca] On Behalf Of Fred E.J. Linton Sent: Sunday, September 03, 2006 2:27 AM To: Categories list Subject: categories: Re: Linear--structure or property? George Janelidze and others answer affirmatively the question > Could you have two (semi)ring structures on the same set with the same > associative multiplication? (attributed to Mike Barr) without ever noticing that the related question, of having two (semi)ring structures on the same set, with the same addition, also has answer YES. For instance, take the additive group of 2x2 matrices with integer entries (or entries from any semiring) and notice that, apart from the usual matrix multiplication, there is also the sophomoric, or pointwise, multiplication (so called since it is generally only sophomores in the first week of their first linear algebra course who, following the analogous pointwise definition of matrix addition, would wish to multiply two matrices by multiplying their corresponding entries). Not quite sure though how this impacts the situation with more than one object. -- Fred ------ Original Message ------ Received: Fri, 11 Aug 2006 01:06:56 PM EDT From: "George Janelidze" To: "Categories list" Subject: categories: Re: Linear--structure or property? > Dear Steve, > > It is true that constructing such examples with more than one object is ... From rrosebru@mta.ca Mon Sep 4 09:32:37 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 04 Sep 2006 09:32:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GKDZD-0000GM-N5 for categories-list@mta.ca; Mon, 04 Sep 2006 09:28:43 -0300 Date: Sun, 03 Sep 2006 23:11:18 -0400 From: "Fred E.J. Linton" To: Subject: categories: Re: Linear--structure or property? Mime-Version: 1.0 Message-ID: <561kiDDks0898S14.1157339478@cmsweb14.cms.usa.net> Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 7 David Ellerman begins, > When a Boolean algebra B is treated as a Boolean ring in the usual ... Boolean algebras actually have the additional surprise that, because their multiplication (meet) is idempotent (as well as commutative and associative), it distributes over itself = ( a(bc) =3D (ab)(ac) ) so that one can use multiplication as = a third addition candidate (the first two having been the = more usual symmetric difference and join, of course). Cheers, and Happy Labor Day (in the US, anyway), -- Fred From rrosebru@mta.ca Mon Sep 4 09:32:37 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 04 Sep 2006 09:32:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GKDZz-0000I4-Jr for categories-list@mta.ca; Mon, 04 Sep 2006 09:29:31 -0300 Date: Mon, 04 Sep 2006 00:14:11 -0400 From: "Fred E.J. Linton" To: "Categories list" Subject: categories: Re: Linear--structure or property? Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 Three items with which to follow up on my earlier note, > For instance, take the additive group of 2x2 matrices with > integer entries (or entries from any semiring) and notice that, > apart from the usual matrix multiplication, there is also > the sophomoric, or pointwise, multiplication ...: 1. In one of the poster sessions at the recent Madrid ICM2006, Camarero, Etayo, Rovira, and Santamaria remind us that the ordinary real plane R^2 (with usual vector addition) admits at least > three distinguished real algebras ... as follows: the set > {a+bi: a, b {/element} R} with i^2 =3D -1, +1, 0, i.e., the > complex, double, and dual numbers. (ICM2006 Abstracts, p. 42) 2. Yefim Katsov (in a telephone conversation) has pointed out that in any reasonable lattice-ordered (semi-)group, where a + (b ^ c) =3D (a+b) ^ (a+c) and a + (b v c) =3D (a+b) v (a+c), one gets two different (semi-)ring structures by using: = as product, the (semi-)group composition + ; and = as sum, in one case the lattice meet ^ , alternatively, the join v . 3. A many-objects version can be concocted from example 2 above by stirring it up with a variant form of Lawvere's observations about metric spaces being categories enriched over an appropriately structured closed monoidal version of the poset R+ of nonnegative real numbers ( order relation > , tensor product + , unit 0 , internal hom the positive part of b-a ). = In detail, if X is a metric space with metric d, consider the ordinary category _X_ whose objects are the points of X while its homsets _X_(p, q) are given by the principal filter (in (R, /=3D d(p, q) } . Composition _X_(p, q) x _X_(q, r) can clearly be given by sending (x, y) to x+y : for identity map is always the number 0, and whenever x >/=3D d(p, q) and y >/=3D d(q, r) we must also have x+y >/=3D d(p, q) + d(q, r) >/=3D d(p, r) . Thus, arithmetic addition provides a composition rule for _X_ , and both real sup and real inf can serve as commutative semigroup structures (across which composition distributes) on the homsets. Of course no one will claim _X_ has any finite (co)products; but, anyway, here any enrichment of _X_ over semigroups is clearly an added item of structure, and not a property of _X_ . -- Fred (and pardon, please, the crude ASCII/TeX symbology) PS: Katsov has also pointed out that a marvelous little New Yorker piece of Fields Medal gossip, turning around Yau, Perelman, Hamilton, and the Poincare conjecture, can be found on the web (for those who don't take the New Yorker, or even those who do) at: http://www.newyorker.com/printables/fact/060828fa_fact2 . -- F. From rrosebru@mta.ca Mon Sep 4 09:32:37 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 04 Sep 2006 09:32:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GKDb4-0000L7-PW for categories-list@mta.ca; Mon, 04 Sep 2006 09:30:39 -0300 From: "Mamuka Jibladze" To: Subject: categories: Morley derivative as non-classical Cantor-Bendixson derivative? Date: Mon, 4 Sep 2006 11:53:05 +0400 MIME-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1"; reply-type=response Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 9 Mention of the Morley derivative by Vaughan Pratt reminded me of my recent suspicion that I think would be natural to share here. Is there a chance to obtain the Morley derivative by performing construction of the Cantor-Bendixson derivative internally on an appropriately chosen internal locale in the topos of set-valued functors on an appropriate subcategory of spaces and continuous maps? Mamuka Jibladze ----- Original Message ----- From: "Vaughan Pratt" To: Sent: Sunday, September 03, 2006 10:59 PM Subject: categories: Re: no membership-respecting morphisms > My request for precursors to Mike Barr's deprecation of set membership > seems to have set loose a thread that has veered off from set theory > into model theory. The following extract from the introduction to > Gerald Sacks' "Saturated Model Theory" (335 pages, W.A. Benjamin, 1972) > serendipitously ties up this loose thread while at the same time > promising that category theory offers deeper insight into categoricity, > a central notion of model theory, than the alternatives. > > "It is true that model theory bears a disheartening resemblance to set > theory, a fascinating branch of mathematics with little to say about > fundamental logical questions, and in particular to the arithmetic of > cardinals and ordinals. But the resemblance is more of manners than of > ideas, because the central notions of model theory are absolute, and > absoluteness, unlike cardinality, is a logical concept. That is why > model theory does not founder on that rock of undecidability, the > generalized continuum hypothesis, and why the Los conjecture is > decidable: A theory T is k-categorical if all models of T of cardinality > k are isomorphic. Los conjectured and Morley proved (Theorem 37.4) that > if a countable theory is k-categorical for some uncountable k, then it > is k-categorical for every uncountable k. The property 'T is > k-categorical for every uncountable k' is of course an absolute property > of T. > > The notion of rank of 1-types was invented by Morley to prove Los's > conjecture. There are proofs of it that make no mention of rank, but > they leave one ill-prepared to prove Shelah's uniqueness theorem > (Section 36). I have made rank a central idea of the book, because it > is the central idea of current model theory. ... Morley's notion of > rank was inspired by the Bendixson differentiation of a closed subset of > a compact Hausdorff space; however, the Morley derivative differs from > the Cantor-Bendixson derivative in that the former commutes with the > inverse limit operation. The Morley derivative is expounded in section > 29 as a transformation which acts on functors of a class common in model > theory. One advantage of a category theoretic treatment of Morley rank > is that it applies equally well to other notions [Shelah] of rank of > 1-types. Section 25 reviews the apparatus of category theory needed in > section 29." > > The difference between this recommendation of category theory for model > theory and (for example) the literature on accessible categories is that > Sacks was not a card-carrying category theorist but a recursion > theorist. While category theory has no bias towards Goedel's notion of > absoluteness (that I'm aware of), it seems reasonable to infer from > Sacks' acceptance of CT that neither is CT biased away from absoluteness > but rather is a neutral general-purpose tool. > > Vaughan Pratt > > > V. Schmitt wrote: >> Dear Paul, as far as i remember model theorists have >> an extremely elegant way of comparing structures: >> no morphisms there but "games" of finite isomorphism >> extensions (see Fraisse' and Ehrenfeucht for the game >> aspect or B.Poizat's book) >> All the first order syntax is subsumed by those games. >> I quite like categories and for sure I do not know everything, >> but I have not seen so far a convincing categorical counterpart >> for these games. >> (And model theory is good stuff!) >> >> Best, >> Vincent. > > > From rrosebru@mta.ca Wed Sep 6 12:26:30 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 06 Sep 2006 12:26:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GKz9G-0000BT-71 for categories-list@mta.ca; Wed, 06 Sep 2006 12:17:06 -0300 Date: Tue, 05 Sep 2006 19:35:11 +0200 From: Ralph Matthes To: categories@mta.ca Subject: categories: CFP MSCS special issue Isomorphisms of Types and Invertibility of Lambda-Terms Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 10 Mathematical Structures in Computer Science Special Issue on Isomorphisms of Types and Invertibility of Lambda-Terms Guest Editors: Ralph Matthes and Sergei Soloviev, Toulouse Call for contributions The study of invertibility of lambda-terms and related subjects such as isomorphisms of types, retractions and subtyping takes an important place in type theory. It is related to number theory, algebra and category theory, and it has applications to information retrieval systems, automatic code generation, data transformation, coding and cryptography. This special issue is a continuation of the series opened by the special issue of MSCS on Isomorphisms of Types published in 2005 (vol. 15, no. 5, Oct. 2005). Partly it is intended as a post-proceedings of WIT2005, a "Types" workshop at IRIT, Toulouse http://www.irit.fr/zeno/WIT2005/, but the contributions are subject to normal refereeing procedure and not limited to the papers presented by the participants of that workshop. Deadlines Deadline for submissions: 6 December 2006 Author's notification: 4 April 2007 Special issue's publication: Winter 2007/Spring 2008 Submissions The submissions should be sent in PDF or Postscript to the guest editors via email: {matthes, soloviev}@irit.fr. Extended versions of work previously published in conference proceedings are eligible for submission but authors should make it clear how their submission improves upon the conference publication; in those cases where Cambridge University Press is not the publisher of the original conference proceedings, authors should take care to avoid infringing that publisher's copyright. Authors who wish to discuss potential submissions are encouraged to contact the guest editors. The Mathematical Structures in Computer Science journal's policy is to impose restrictions in advance neither on the number of papers nor their length. However, as the special issue will contain approximately 180 pages, it is anticipated that it will contain a mixture of papers of between 15 and 45 pages. From rrosebru@mta.ca Wed Sep 6 14:43:40 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 06 Sep 2006 14:43:40 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GL1NX-0001cU-Pi for categories-list@mta.ca; Wed, 06 Sep 2006 14:40:00 -0300 Date: Wed, 6 Sep 2006 13:40:35 -0400 (EDT) From: Richard Blute To: categories@mta.ca Subject: categories: Octoberfest-Call for Participation MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 11 Call for Participation-Octoberfest 2006 +++++++++++++++++++++++++++++++++++++++++ As already announced, Octoberfest will be hosted by the Logic and Foundations of Computing group (LFC) at the University of Ottawa, on the weekend of October 21st and 22nd. See the Octoberfest website at http://www.site.uottawa.ca/~phil/lfc/. We would like to now invite submissions for talks. Please send a title and short abstract to Rick Blute at rblute@mathstat.uottawa.ca. The deadline for submission is September 22th, and we will post a schedule soon after that. Here is the hotel information again. There will also be further information on lodging on the website. Lodging Information: ******************** We have booked a block of rooms at: Quality Hotel Downtown Ottawa 290 Rideau Street Ottawa, ON K1N 5Y3 (P) 613-789-7511 These rooms are held for Friday and Saturday nights. The group number is 105626 and the group name is "Ottawa U-Math Dept". The rate is $99.00 plus tax. Guests may phone the hotel directly at 613-789-7511 to reserve and may quote either the group name or number to get the preferred rate. The cutoff for this special rate is September 20th, but we strongly advise you not to wait that long. Here is a list of B&B's near Ottawa U, in random order: Home Sweetland Home B&B: 62 Sweetland Avenue, Ottawa, ON K1N 7T6 Phone: (613) 234-1871 Reservations: 1-877-299-3499 (web: http://www.homesweetlandhome.ca) Benners B&B 541 Besserer 613-789-8320 (web: http://www.bennersbedandbreakfast.com) Gasthaus Switzerland Inn 89 Daly Avenue Ottawa ON K1N6E6 613-237-0335 (www.gasthausswitzerlandinn.com) Ottawa Centre Bed and Breakfast 62 Stewart Street Ottawa, Ontario K1N 6J1 Phone: 613-237-9494 Toll Free: 866-240-4659 (web: http://www.ottawacenterbnb.com) Hope to see you all then: Rick Blute Phil Scott -- From rrosebru@mta.ca Fri Sep 8 11:49:33 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 08 Sep 2006 11:49:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GLhY8-0003Td-Tl for categories-list@mta.ca; Fri, 08 Sep 2006 11:41:45 -0300 Date: Fri, 08 Sep 2006 11:23:11 +0100 From: Prof T Porter MIME-Version: 1.0 To: Categories list Subject: categories: many object cobar constructions Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 12 Dear All, I have been trying to compare the simplicially enriched category/Segal-category approach to weak categories and the dg-category/$A_\infty$-category approach coming from derived categories etc. It is clear that there is a cobar construction leading from a dg-cocategory to a dg-category and results on twisting cochains also go across with no difficulty. I am therefore surprised that I cannot find an explicit reference for this in the literature (probably I have not loked in the right place as it is in an `overlap' area!). Can anyone help with some good references? Also has anyone given a good interpretation of the twisting cochains and the twisted tensor of modules in this setting. I know of the usual interpretations. Perhaps someone who knows the string theoretic links may have an idea. Thanks, Tim Porter From rrosebru@mta.ca Fri Sep 8 11:49:33 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 08 Sep 2006 11:49:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GLhX1-0003Mu-2v for categories-list@mta.ca; Fri, 08 Sep 2006 11:40:35 -0300 Mime-Version: 1.0 Message-Id: Date: Fri, 8 Sep 2006 11:08:47 +0200 To: categories@mta.ca From: Anders Kock Subject: categories: preprint: Connections and path connections in groupoids Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 13 Dear all, This is to announce the availability of a preprint "Connections and path connections in groupoids". Abstract: We describe two gauge theoretic notions of connection in a (differentiable) groupoid. The two notions are related via the notion of holonomy. Holonomy formation (integration) is shown to be inverse of a certain differentiation process. The method is that of Synthetic Differential Geometry, notably in the form of "First Neighbourhood of the Diagonal". The preprint can be dowlnoaded from http://www.imf.au.dk/publs?id=619 or from my home page http://home.imf.au.dk/kock/ Yours Anders From rrosebru@mta.ca Fri Sep 8 16:30:34 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 08 Sep 2006 16:30:34 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GLlxo-0003rJ-F5 for categories-list@mta.ca; Fri, 08 Sep 2006 16:24:32 -0300 Date: Fri, 8 Sep 2006 18:56:05 +0200 From: "Urs Schreiber" To: categories@mta.ca Subject: categories: Re: preprint: Connections and path connections in groupoids MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 On 9/8/06, Anders Kock wrote: > This is to announce the availability of a preprint > "Connections and path connections in groupoids". This is very nice! I have posted a small discussion of this preprint here: http://golem.ph.utexas.edu/category/2006/09/kock_on_connections.html From rrosebru@mta.ca Fri Sep 8 16:30:34 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 08 Sep 2006 16:30:34 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GLlyN-0003u3-Q7 for categories-list@mta.ca; Fri, 08 Sep 2006 16:25:07 -0300 Date: Fri, 08 Sep 2006 19:46:13 +0200 From: fritsch@math.lmu.de To: categories@mta.ca Subject: categories: Ulrich Seip MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 Dear colleagues, with deep regret I have to inform that my friend and colleague Ulrich Seip passed away on Saturday, September 1, 2006 at the age of 69. Yours Rudolf Fritsch From rrosebru@mta.ca Sun Sep 10 21:39:29 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 10 Sep 2006 21:39:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GMZjF-0003GQ-Uo for categories-list@mta.ca; Sun, 10 Sep 2006 21:32:49 -0300 Date: Sat, 09 Sep 2006 14:28:02 +0200 From: fritsch@math.lmu.de To: categories@mta.ca Subject: categories: Ulrich Seip MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 Dear colleagues, I was so confused by the bad news of yesterday that I mixed the dates. Ulrich died on Saturday, September 2, 2006 in Berlin (Germany). yours Rudolf From rrosebru@mta.ca Sun Sep 10 21:39:29 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 10 Sep 2006 21:39:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GMZiU-0003EB-DJ for categories-list@mta.ca; Sun, 10 Sep 2006 21:32:02 -0300 Date: Sat, 9 Sep 2006 16:28:00 -0300 (ADT) From: Bob Rosebrugh To: categories Subject: categories: Easik - software for categorical database design MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 17 This announces the release of Easik, a Java application providing a graphical design environment for Entity-Attribute (EA) sketches. These sketches are the syntactic basis for the categorical Sketch Data Model (SkDM) which extends and enhances the standard Entity-Relationship-Attribute data model. For extensive information about the Sketch Data Model consult the web sites of the poster and Michael Johnson. Complementing its graphical interface, Easik can save an EA sketch design into an XML document which is exportable to a database schema in SQL. The schema includes triggers and procedures to enforce the constraints defined graphically. Easik provides connectivity to common database management systems via JDBC. The application is available for download at http://mathcs.mta.ca/research/rosebrugh/Easik or follow links from http://www.mta.ca/~rrosebru/ Instructions for using Easik are are on the Web pages: - users may download a Java archive (jar file) providing the application and - source code is available. Easik was developed by Robert Fletcher, Kevin Green, Vera Ranieri and Robert Rosebrugh with support from NSERC Canada and Mount Allison University. We are interested comments from users, and would also appreciate receiving reports of difficulties with function or usability. Bob Rosebrugh From rrosebru@mta.ca Fri Sep 15 12:16:47 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 15 Sep 2006 12:16:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GOFIU-0005VN-Ng for categories-list@mta.ca; Fri, 15 Sep 2006 12:08:06 -0300 Date: Fri, 15 Sep 2006 15:04:36 +0200 From: "S. Mantovani" To: categories@mta.ca Subject: categories: Milan Workshop in Categorical algebra, second announcement Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 18 ********************************************** INTERNAL ACTIONS and INTERNAL STRUCTURES * WORKSHOP in CATEGORICAL ALGEBRA * ********************************************** Second announcement Dear Colleagues, the Workshop will be held at the Department of Mathematics of the Universit=E0 degli Studi of Milan, from 26th to 28th o= f October, 2006. The purpose of the workshop is to consider the notion of internal action in different categorical contexts and to relate it with internal structures defined thereby. In particular, the well established context of semiabelian categories provides a natural setting for studying the interplay between categorical and algebraic aspects of actions, with respect to internal structures that may be defined. The workshop is intended to reflect its etymology, in order to give the participants a fruitful opportunity of debate and exchange experiences about the subject. NEWS: The web pages http://users.mat.unimi.it/users/mantovani/workshopMi06.htm have been updated and now they include: - an online inscription form to partecipate to the workshop - abstracts of the lectures - maps, logistics and directions Furthermore, it is still possible to submit contributions on related topics. For any question, please contact the organizers at milanworkshop.06@gmail.com Best regards, Stefano Kasangian Sandra Mantovani Beppe Metere -- Sandra Mantovani Dipartimento di Matematica Via C. Saldini, 50 20133 Milano Tel 02 50316137 Fax 02 50316090 Sandra.Mantovani@mat.unimi.it http://users.mat.unimi.it/~mantovani From rrosebru@mta.ca Fri Sep 15 12:16:47 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 15 Sep 2006 12:16:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GOFHu-0005Rc-CR for categories-list@mta.ca; Fri, 15 Sep 2006 12:07:30 -0300 From: J=FCrgen Koslowski Subject: categories: PSSL84, second announcement To: categories@mta.ca (categories list) Date: Fri, 15 Sep 2006 13:02:20 +0200 (CEST) MIME-Version: 1.0 Content-Type: text/plain; charset=3Diso-8859-1 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 PERIPATETIC SEMINAR ON SHEAVES AND LOGIC 84th meeting - second announcement Dear Colleagues, As most of you will already know, the 84th meeting of the seminar=3D20 takes place at the Department of Theoretical Computer Science of the Technical University Braunschweig, Germany, over the weekend of October 14-15, 2006. As always, the seminar welcomes talks using or addressing category theory or logic, either explicitly or implicitly, in the study of any aspect of mathematics or science. Samson Abramsky and Bob Coecke have agreed to give a series of three lectures on catgorical aspects of quantum informatics. In addition, we can now confirm the participation of professor Reinhard Werner, mathematical physicist at the TU Braunschweig with special interest in this field. Braunschweig is located about 60 km East of Hannover and about 200 km West of Berlin. It can easily be reached by car or train. The closest airport is in Hannover; the train to Hannover's main station takes about 20 minutes, and the train from there to Braunschweig takes about 40 minutes. Further information on the location of the seminar, along with details on local travel together with an online registration form can be found at =09http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/PSSL84.html You will also find links to two hotels offering special university rates, but you should register by the end of September. Best regards, Jiri Adamek J=3DFCrgen Koslowski Stefan Milius --=3D20 Juergen Koslowski If I don't see you no more on this world ITI, TU Braunschweig I'll meet you on the next one koslowj@iti.cs.tu-bs.de and don't be late! http://www.iti.cs.tu-bs.de/~koslowj Jimi Hendrix (Voodoo Child, SR) From rrosebru@mta.ca Fri Sep 15 12:16:47 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 15 Sep 2006 12:16:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GOFHR-0005Nv-5J for categories-list@mta.ca; Fri, 15 Sep 2006 12:07:01 -0300 Date: Thu, 14 Sep 2006 16:43:32 -0400 From: Walter Tholen MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Summerschool Haute Bodeux June 2007 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 20 Dear category theorist- Below is a reminder for the "Summer School on Contemporary Categorical=20 Methods in Algebra and Topology". Anybody interested to participate in=20 the School is encouraged to email me before the end of this month.=20 Suggestions for contributed papers will also be considered by the=20 Scientific Committee. The info is also available on my webpage at http://www.math.yorku.ca/~tholen/ Regards, Walter Tholen. SUMMER SCHOOL ON CONTEMPORARY CATEGORICAL METHODS IN ALGEBRA AND TOPOLOGY Haute-Bodeux, Belgium, 3-10 June 2007 In the tradition of previous meetings held at this location, a Summer=20 School on Contemporary Categorical Methods in Algebra and Topology will=20 be held in Haute-Bodeux, a village in the Ardennes region of south-east=20 Belgium, from June 3 (arrival day) until June 10, 2007 (departure day).=20 Participants will stay in the "Hostellerie Doux-Repos" http://hotels.belgium-bookings.com/hotel/be/hostellerie-doux-repos.html?l= abel=3Dgl-hotels-Hostellerie-Doux-Repos or nearby guestrooms, all meals will be taken in the Hostellerie - which=20 is known for its excellent cuisine. The primary aim of the meeting is to=20 provide students and young researchers who already have a working=20 knowledge of categories with an opportunity to learn about various=20 topics of interest in categorical algebra and topology, including - categorical and topological aspects of semi-abelian theories, - categorical descent and Galois theory, - accessible categories and their applications to homotopy theory, - lax-algebraic methods in categorical topology. However, more established researchers in nearby fields who wish to=20 enhance their knowledge on these topics or present a paper are also=20 welcome. Lecture series will be given by the following researchers who=20 constitute the Scientific Committee of the meeting: - Maria Manuel Clementino - Dominique Bourn - George Janelidze - Jiri Rosicky - Walter Tholen. The local organizer of the Summer School is Francis Borceux (Universit=E9= =20 Catholique de Louvain). It is estimated that the total cost of the=20 meeting will be about 975 Euros per person: this covers the registration=20 fee, transportation from and to Brussels airport or Li=E8ge railway=20 station (on the designated arrival and departure days), accommodation=20 and meals (including conference dinner and drinks with meals), social=20 activities and an excursion (excluding dinner on the excursion day).=20 Unfortunately, the organizers do not have funds available to provide any=20 financial support. Accommodation in Haute-Bodeux is strictly limited, and attendance at the=20 meeting will be by invitation only. However, anyone who wishes to be=20 considered for invitation, or to propose names of people who might be=20 invited, is asked to send an e-mail to Walter Tholen=20 before the=20 end of September 2006. It is expected that invitations will be sent out=20 early in November 2006. Those invited will be sent formal letters of=20 invitation to assist them in obtaining funding, and will also be=20 provided with a reading list of material which may be assumed in the=20 Summer School lectures. From rrosebru@mta.ca Sat Sep 16 16:05:19 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 16 Sep 2006 16:05:19 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GOfLZ-0003IX-P0 for categories-list@mta.ca; Sat, 16 Sep 2006 15:57:01 -0300 Date: Fri, 15 Sep 2006 20:44:01 -0400 From: jim stasheff MIME-Version: 1.0 To: Categories List Subject: categories: from the n-category cafe' Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 21 http://golem.ph.utexas.edu/category/2006/09/groupoids_and_stacks_in_physic.html#comments Groupoids and Stacks in Physics and Geometry Posted by John Baez MathML-enabled post (click for more details). From January 8th to April 6th of 2007, the Institut Henri Poincar=E9 will be running a program on: * Groupoids and Stacks in Physics and Geometry If you don=92t know about groupoids and stacks, or even if you do, try th= is overview of the subject. MathML-enabled post (click for more details). The program on Groupoids and Stacks in Physics and Geometry will feature=20 the following workshops: * Higher structures in geometry and physics (Jan 15-Jan 19) Organizers: Alberto Cattaneo and Ping Xu * Quantum cohomology of stacks and string theory (Feb 12-Feb 16) Organizers: Kai Behrend, Barbara Fantechi and Andrew Kresch * Groupoids in operator algebras and noncommutative geometry (Feb 26-Mar 2) Organizers: Jean Renault and Jean-Louis Tu There will also be a number of long courses, including: * Kai Behrend and Andrew Kresch, Introduction to stacks * Lawrence Breen, Categorical Structures and cohomology * Jean-Louis Tu, Operator Algebras, K-theory and groupoids (abstract)(r=E9sum=E9) * Ping Xu, Lie groupoids and Poisson geometry (abstract) Some support is available for grad students to attend - see the program=20 website. Posted at September 13, 2006 8:30 AM UTC From rrosebru@mta.ca Mon Sep 18 15:08:42 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 18 Sep 2006 15:08:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GPNQg-0001Ws-3g for categories-list@mta.ca; Mon, 18 Sep 2006 15:01:14 -0300 Date: Sun, 17 Sep 2006 23:38:34 -0300 (BRT) From: Ruy de Queiroz To: wollic@cin.ufpe.br Subject: categories: WoLLIC'2007 - Call for Papers MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 22 [** sincere apologies for duplicates **] Call for Papers 14th Workshop on Logic, Language, Information and Computation (WoLLIC'2007) Rio de Janeiro, Brazil July 2-5, 2007 WoLLIC is an annual international forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning. Each meeting includes invited talks and tutorials as well as contributed papers. The Fourteenth WoLLIC will be held in Rio de Janeiro, Brazil, from July 2 to July 5, 2007, and sponsored by the Association for Symbolic Logic (ASL), the Interest Group in Pure and Applied Logics (IGPL), the European Association for Logic, Language and Information (FoLLI), the European Association for Theoretical Computer Science (EATCS), the Sociedade Brasileira de Computacao (SBC), and the Sociedade Brasileira de Logica (SBL). PAPER SUBMISSION Contributions are invited on all pertinent subjects, with particular interest in cross-disciplinary topics. Typical but not exclusive areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection. Proposed contributions should be in English, and consist of a scholarly exposition accessible to the non-specialist, including motivation, background, and comparison with related works. They must not exceed 10 pages (in font 10 or higher), with up to 5 additional pages for references and technical appendices. The paper's main results must not be published or submitted for publication in refereed venues, including journals and other scientific meetings. It is expected that each accepted paper be presented at the meeting by one of its authors. Papers must be submitted electronically at www.cin.ufpe.br/~wollic/wollic2007/instructions.html A title and single-paragraph abstract should be submitted by February 23, and the full paper by March 2 (firm date). Notifications are expected by April 13, and final papers for the proceedings will be due by April 27 (firm date). PROCEEDINGS Proceedings, including both invited and contributed papers, will be published in advance of the meeting. Publication venue TBA. INVITED SPEAKERS: TBA STUDENT GRANTS ASL sponsorship of WoLLIC'2007 will permit ASL student members to apply for a modest travel grant (deadline: April 1, 2007). See www.aslonline.org/studenttravelawards.html for details. IMPORTANT DATES February 23, 2007: Paper title and abstract deadline March 2, 2007: Full paper deadline (firm) April 12, 2007: Author notification April 26, 2007: Final version deadline (firm) PROGRAM COMMITTEE Samson Abramsky (U Oxford) Michael Benedikt (Bell Labs) Lars Birkedal (ITU Copenhagen) Andreas Blass (U Michigan) Thierry Coquand (Chalmers U, Goteborg) Jan van Eijck (CWI, Amsterdam) Marcelo Finger (U Sao Paulo) Rob Goldblatt (Victoria U, Wellington) Yuri Gurevich (Microsoft Redmond) Hermann Haeusler (PUC Rio) Masami Hagiya (Tokyo U) Joseph Halpern (Cornell U) John Harrison (Intel UK) Wilfrid Hodges (U London/QM) Phokion Kolaitis (IBM Almaden Research Center) Marta Kwiatkowska (U Birmingham) Daniel Leivant (Indiana U) (Chair) Maurizio Lenzerini (U Rome) Jean-Yves Marion (LORIA Nancy) Dale Miller (Polytechnique Paris) John Mitchell (Stanford U) Lawrence Moss (Indiana U) Peter O'Hearn (U London/QM) Prakash Panangaden (McGill, Montreal) Christine Paulin-Mohring (Paris-Sud, Orsay) Alexander Razborov (Steklov, Moscow) Helmut Schwichtenberg (Munich U) Jouko Vaananen (U Helsinki) ORGANISING COMMITTEE Marcelo da Silva Correa (U Fed Fluminense) Renata P. de Freitas (U Fed Fluminense) Ana Teresa Martins (U Fed Ceara') Anjolina de Oliveira (U Fed Pernambuco) Ruy de Queiroz (U Fed Pernambuco, co-chair) Petrucio Viana (U Fed Fluminense, co-chair) WEB PAGE www.cin.ufpe.br/~wollic/wollic2007 From rrosebru@mta.ca Wed Sep 20 13:43:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 20 Sep 2006 13:43:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GQ4yy-0001UV-Vg for categories-list@mta.ca; Wed, 20 Sep 2006 13:31:33 -0300 Date: Wed, 20 Sep 2006 10:38:14 -0400 (EDT) From: Richard Blute To: categories@mta.ca Subject: categories: Octoberfest deadlines MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 23 Hi everyone, There are several deadlines fast approaching for people attending Octoberfest. Today, September 20th, is the last official day to get the reduced rate at the Quality Hotel, and Friday, September 22nd is the last day to submit an abstract for a talk. Abstracts should be submitted to Rick Blute at rblute@mathstat.uottawa.ca. (I will reply when I receive your abstract.) See our website for full details, including further accomodation info. http://aix1.uottawa.ca/~scpsg/Octoberfest06/Octoberfest06.prelim2.html See you all soon, Rick Blute Phil Scott From rrosebru@mta.ca Fri Sep 22 14:12:17 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 22 Sep 2006 14:12:17 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GQoOJ-0006BK-SM for categories-list@mta.ca; Fri, 22 Sep 2006 14:00:43 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: MFPS XXIII Call for Papers Date: Thu, 21 Sep 2006 11:46:38 -0500 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 24 CALL FOR PAPERS MFPS XXIII Twenty-third Conference on the Mathematical Foundations of Programming Semantics Tulane University New Orleans, LA USA April 11 - 14, 2007 Partially Supported by US Office of Naval Research The Twenty-third Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIII) will take place on the campus of Tulane University, New Orleans, LA USA from Wednesday, April 11 through Saturday, April 14, 2007. The MFPS conferences are devoted to those areas of mathematics, logic, and computer science which are related to models of computation, in general, and to the semantics of programming languages, in particular. The series has particularly stressed providing a forum where researchers in mathematics and computer science can meet and exchange ideas about problems of common interest. As the series also strives to maintain breadth in its scope, the conference strongly encourages participation by researchers in neighboring areas. The INVITED SPEAKERS for MFPS XXIII are Gerard Berry (Esterel Technologies) --- to be confirmed --- Stephen Brookes (CMU) Jane Hillston (Edinburgh) John Mitchell (Stanford) Gordon Plotkin (Edinburgh) John Power (Edinburgh) In addition, there will be three special sessions: 1. A special session honoring GORDON PLOTKIN on his 60th birthday year, organised by Samson Abramsky (Oxford). 2. A special session on SECURITY, organised by Catherine Meadows (NRL). 3. A special session on SYSTEMS BIOLOGY, organised by Jane Hillston (Edinburgh) and Prakash Panangaden (McGill). 4. A Special Session on Physics, Information and Computation organized by Keye Martin (NRL). Further, there will be a TUTORIAL DAY on April 11. The topic will be Domain Theory; the speakers will be announced at a later date. This event will be free to those who are interested in attending. The remainder of the program will consist of papers selected by the following PROGRAM COMMITTEE Samson Abramsky (Oxford) Michael Mislove (Tulane) Andrej Bauer (Ljubljana) John Mitchell (Stanford) Stephen Brookes (CMU) Eugenio Moggi (Genova) Pierre-Louis Curien (CNRS & Paris 7) Laurent Regnier (Marseille) Andrzej Filinski (Copenhagen) Giuseppe Rosolini (Genova) Marcelo Fiore (Cambridge), CHAIR Davide Sangiorgi (Bologna) Achim Jung (Birmingham) Philip Scott (Ottawa) Masahito Hasegawa (Kyoto) Daniele Varacca (Paris 7) Ursula Martin (QM London) James Worrell (Oxford) Catherine Meadows (NRL) Steve Zdancewic (Pennsylvania) from submissions received in response to this call for papers. TOPICS include, but are not limited to, the following: biocomputation; categorical models; concurrent and distributed computation; constructive mathematics; domain theory; formal languages; formal methods; game semantics; lambda calculus; logic; non-classical computation; probabilistic systems; process calculi; program analysis; programming- language theory; quantum computation; rewriting theory; security; specifications; topological models; type systems; type theory. The CONFERENCE PROCEEDINGS will be published by ENTCS (Electronic Notes in Theoretical Computer Science ). Submission instructions, style files for preparing a submission, and a link to the MFPS XXIII submission site are available from the conference web page: http://www.math.tulane.edu/~mfps/mfps23.htm IMPORTANT DATES: * Fri Dec 15: Paper registration deadline, with short abstracts. * Fri Dec 22: Paper submission deadline. * Fri Feb 4: Author notification. * Fri Mar 2: Final versions for the proceedings. The Organising Committee for MFPS consists of Stephen Brookes (CMU), Achim Jung (Birmingham), Catherine Meadows (NRL), Michael Mislove (Tulane), and Prakash Panangaden (McGill). The local arrangements for MFPS XXIII are being overseen by Michael Mislove. =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA =============================================== From rrosebru@mta.ca Mon Sep 25 20:38:45 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 25 Sep 2006 20:38:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GRzrs-0007Qt-QJ for categories-list@mta.ca; Mon, 25 Sep 2006 20:28:08 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca From: Steve Vickers Subject: categories: Are geometric categories balanced? Date: Mon, 25 Sep 2006 20:47:37 +0100 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 25 Am I right in believing that geometric categories (Elephant A 1.4.18) need not be balanced? (I don't know a counterexample - the geometric categories that I can think of are all toposes.) The reason I ask is this. One is (or certainly I am) used to thinking of geometric logic as the logic of Grothendieck toposes. Grothendieck toposes are balanced, and consequently a sound reasoning principle in their internal logic is that functions are equivalent to total, single-valued relations. One therefore thinks of this as a principle of geometric reasoning. However, I suspect it doesn't follow just from the pure logic - the connectives and inference rules - of geometric logic. This would be verified if there are unbalanced geometric categories, since the pure logic is interpretable in arbitrary geometric categories. I would take this as indicating that we want geometric logic to be more than just what the pure logic says it is. The Elephant gives two different definitions of geometric theory: by the pure logic in D 1.1.6, and by a more general notion of geometric construct in B 4.2.7. It asserts their equivalence, but I think this must be with respect to a semantics already presumed to be in Grothendieck toposes. Steve Vickers. From rrosebru@mta.ca Tue Sep 26 08:00:18 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 26 Sep 2006 08:00:18 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GSAcl-00056D-8u for categories-list@mta.ca; Tue, 26 Sep 2006 07:57:15 -0300 Date: Tue, 26 Sep 2006 08:51:41 +0100 (BST) From: "Prof. Peter Johnstone" To: categories@mta.ca Subject: categories: Re: Are geometric categories balanced? Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 On Mon, 25 Sep 2006, Steve Vickers wrote: > Am I right in believing that geometric categories (Elephant A 1.4.18) > need not be balanced? (I don't know a counterexample - the geometric > categories that I can think of are all toposes.) > Of course -- (cocomplete) quasitoposes are geometric categories as well, and they needn't be balanced. Incidentally, Gordon Monro wrote a couple of papers about the interpretation of logic in quasitoposes, which appeared in JPAA 42 (1986). > The Elephant gives two different definitions of geometric theory: by > the pure logic in D 1.1.6, and by a more general notion of geometric > construct in B 4.2.7. It asserts their equivalence, but I think this > must be with respect to a semantics already presumed to be in > Grothendieck toposes. > I've never really found a satisfactory conceptual explanation of why these two definitions come out equivalent. Undoubtedly it's connected with the fact that, in the recursive definition, one is thinking in terms of interpretations in geometric categories, but is there more to it than that? Peter Johnstone From rrosebru@mta.ca Wed Sep 27 14:37:03 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 27 Sep 2006 14:37:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GSdCJ-0005D2-2X for categories-list@mta.ca; Wed, 27 Sep 2006 14:27:51 -0300 Date: Wed, 27 Sep 2006 15:24:07 +0200 (CEST) From: Erik Palmgren To: categories@mta.ca MIME-Version: 1.0 Subject: categories: Workshop on Identity Types Content-Type: TEXT/PLAIN; CHARSET=ISO-8859-1; FORMAT=flowed Content-ID: Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 27 Identity Types - Topological and Categorical Structure Workshop, November 13-14, 2006, Uppsala University. The identity type, the type of proof objects for the fundamental propositional equality, is one of the most intriguing constructions of intensional dependent type theory (also known as Martin-L=F6f type theory). Its complexity became apparent with the Hofmann-Streicher groupoid model of type theory. This model also hinted at some possible connections between type theory and homotopy theory and higher categories. Exploration of his connection is intended to be the main theme of this workshop. Preliminary list of speakers Steve Awodey (Pittsburgh) Peter Dybjer (G=F6teborg) Richard Garner (Uppsala) Martin Hyland (Cambridge, to be confirmed) Per Martin-L=F6f (Stockholm) Thomas Streicher (Darmstadt) Michael A Warren (Pittsburgh) A final list of speakers will be prepared shortly before the workshop. If you are interested in giving a talk, please submit a short abstract to the organiser before October 25. The working days of the meeting are November 13 and November 14 until noon. Organiser: Erik Palmgren, Uppsala University, email: palmgren@math.uu.se Venue: Uppsala University, Polacksbacken, L=E4gerhyddsv=E4gen 1-2, Uppsala, Sweden. Accomodation is expected to be arranged by the participants themselves. See the workshop webpage for a list of recommended hotels and further information. Workshop webpage: www.math.uu.se/~palmgren/itt From rrosebru@mta.ca Fri Sep 29 15:41:50 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 29 Sep 2006 15:41:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GTN8N-0001pd-OL for categories-list@mta.ca; Fri, 29 Sep 2006 15:30:51 -0300 Date: Fri, 29 Sep 2006 13:40:53 -0400 From: tholen@mathstat.yorku.ca To: categories@mta.ca Subject: categories: papers available MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;format="flowed" Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 28 I have made the following recent papers available from my home page at www.math.yorku.ca/~tholen I appreciate receiving any comments that you may have. Regards, Walter. ------------------------------------- Marco Grandis and Walter Tholen: Natural weak factorization systems Abstract. In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category K is introduced, as a pair (comonad, monad) over K^2. The link with existing notions in terms of morphism classes is given via the respective Eilenberg-Moore categories. ------------------------------------- Jiri Rosicky and Walter Tholen: Factorization, fibration and torsion Abstract. A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3-for-2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and of weak factorization system, as used in abstract homotopy theory. ------------------------------------- Eraldo Giuli and Walter Tholen: A topologist's view of Chu spaces Abstract. For a symmetric monoidal-closed category X and any object K, the category of K-Chu spaces is small-topological over X and small-cotopological over X^op. It's full subcategory of M-extensive K-Chu spaces is topological over X when X is M-complete, for any morphism class M. Often they form a full coreflective subcategory of Diers' category of affine K-spaces. Hence, in addition to their roots in in the theory of pairs of topological vector spaces (Barr) and in the study of event structures for modeling concurrent processes (Pratt), Chu spaces seem to have a less explored link with algebraic geometry. We use the Zariski closure operator to characterize the self-dual category of M-extensive and M-coextensive K-Chu spaces.