Date: Sat, 1 Oct 1994 12:45:22 +0500 (GMT+4:00)
Subject: ??? coherent , T_{0} => sober ???
Date: Sat, 1 Oct 1994 05:23:38 +0100
From: Maria Joao Frade
Dear Group,
I would be very greatful if someone could help me to make clear the following
situation (doubt) :
In article "Domain Theory in Logical Form" (1991) S. Abramsky says
(definition 2.3.2) that
a space X is coherent if the \Omega(X) is a coherent local
and in theorem 2.3.3 (iii) he writes
CohSp \simeq CohLoc \simeq DLat^{op}
where CohSp is the category of coherent T_{0} spaces, and continuous
maps which preserve compact-open subsets under inverse image.
But, in Johnstone's book "Stone Spaces" (1982) it is written (II.3.4)
that
a space X is coherent if it is sober and \Omega(X) is a coherent local
and in the corollary (Stone's representation theorem for distributive
lattices) he writes
The category DLat is dual to the category CohSp of coherent spaces
and coherent maps between them.
>From the above definitions and results, I wonder if the following
result is true:
If the space X is T_{0} and \Omega(X) is a coherent local
then the space X is sober
I have looked around and I didn't find that result. Am I
misunderstanding something ?
I'm finishing my MSc. thesis on "Behavior and State" and for the
work I'm developing a result like the above would be very helpful.
So, I would be very greatful if you could help me.
Thanks in advance for time and trouble,
Maria Joao Frade
------------------------------------------------------
Maria Joao Gomes Frade e-mail: mjf@di.uminho.pt
Assistant Lecturer and MSc. student
Departamento de Informatica, Universidade do Minho
Date: Mon, 3 Oct 1994 00:20:30 +0500 (GMT+4:00)
Subject: Computing: the Australian Theory Seminar
Date: Mon, 3 Oct 1994 09:47:10 +1000
From: Barry Jay
Computing: the Australian Theory Seminar (CATS)
Sydney
17th-19th December, 1994
Sponsord by
The Key Centre for Advanced Computing Sciences
University of Technology, Sydney
FIRST ANNOUNCEMENT
CATS will be open to all aspects of the theory of
computer science. It will provide an opportunity for
the scattered community of computing theorists in
Australia and New Zealand to meet and exchange views
in an informal setting. The following international
visitors will be coming.
Robin Cockett (Calgary)
Eugenio Moggi (Genoa)
Maurice Nivat (France)
Phil Wadler (Glasgow)
Printed proceedings will be provided.
Following the meeting, authors will be invited to submit revised papers
for a special issue of Theoretical Computer Science on Australian
research.
PROGRAM COMMITTEE
John Crossley
Barry Jay (Chair)
John Staples
SUBMISSIONS should be no more than twelve pages, include the author's
name(s) and e-mail addresses, and be received by Friday, 4th November.
Electronic submission in postscript format is preferred. Send them to
cats@socs.uts.edu.au. Hard copy should be sent to Dr C.B. Jay, School
of Computing Sciences, University of Technology, Sydney, PO Box 123
Broadway, 2007.
NOTIFICATION of acceptance will be sent out by Friday, 2nd December.
Pre-conference drinks on Friday
evening, and a conference dinner on Sunday will be
included in the registration costs.
REGISTRATION
Before 15/11/94 $85
After 15/11/94 $120
Students (before 15/11) $45
ACCOMMODATION
A limited number of rooms in new university
appartments with shared facilities are available for
$40 per night. These will be allocated in order of
request.
ENQUIRIES
Send enquiries to cats@socs.uts.edu.au
(not the sender of this message).
Please distribute this announcement widely.
Barry Jay
------------------------------------------------------
-------------- REGISTRATION FORM ---------------------
------------------------------------------------------
FAMILY NAME___________________________________________
GIVEN NAMES __________________________________________
STUDENT YES/NO
ACCOMMODATION REQUIRED 16/12 17/12 18/12 19/12
(circle dates)
REGISTRATION FEE _____________________________________
(Make checks payable to C.A.T.S.)
Please post your registration form to:
CATS c/o
Dr C.B. Jay
School of Computing Sciences
University of Technology, Sydney
P.O. Box 123 Broadway
Australia. 2007
Date: Mon, 3 Oct 1994 16:51:35 +0500 (GMT+4:00)
Subject: Re: ??? coherent , T_{0} => sober ???
Date: Mon, 3 Oct 1994 10:56:46 +0000
From: Steven Vickers
>In article "Domain Theory in Logical Form" (1991) S. Abramsky says
>(definition 2.3.2) that
>
> a space X is coherent if the \Omega(X) is a coherent local
>
>and in theorem 2.3.3 (iii) he writes
>
> CohSp \simeq CohLoc \simeq DLat^{op}
>
>where CohSp is the category of coherent T_{0} spaces, and continuous
>maps which preserve compact-open subsets under inverse image.
>
>
>But, in Johnstone's book "Stone Spaces" ... [standard defns omitted]
>
>>From the above definitions and results, I wonder if the following
>result is true:
> If the space X is T_{0} and \Omega(X) is a coherent local
> then the space X is sober
The standard definitions of coherent - or spectral - space (e.g. Hochster's
in Trans AMS 142, 1969) clearly include sobriety as part of the definition
(in Hochster: every closed irreducible subspace has a generic point), and
that "T_0 + Omega X coherent" is insufficient.
For a counterexample, let D be the Kahn domain of finite and infinite bit
streams (i.e. order is prefix order, topology is Scott), and let D' be the
subspace formed by removing a single infinite point. The inclusion D' -> D
gives an isomorphism between Omega D' and Omega D, which is coherent, and
D' is T_0. However, D' is not sober, because it lacks the point that was
taken out.
I think therefore that Samson's Defn 2.3.2 ought to be modified to include
sobriety as part of the definition, and that Theorem 2.3.3 needs mild
rewording (e.g. delete "T_0"). Apart from that, I'd be very surprised if
there's anything else in the whole paper that has to be changed as a
result.
Steve Vickers.
Date: Mon, 3 Oct 1994 16:54:17 +0500 (GMT+4:00)
Subject: Re: ??? coherent , T_{0} => sober ???
Date: Mon, 3 Oct 1994 11:32:58 +0100 (BST)
From: Samson Abramsky
I'm afraid this was a slip of the pen on my part. I should have included
sobriety in the definition of coherent space (and then omitted T_0 in
2.3.3(iii)).
This is what comes of trying to be ``helpful'' ...
I included this material as general background only. Theorem 2.3.3 is
never used in the remainder of the paper.
Samson Abramsky
Date: Mon, 3 Oct 1994 16:57:36 +0500 (GMT+4:00)
Subject: query of M.J.Frade
Date: Mon, 3 Oct 94 14:27:29 -0500
From: James Madden
In response to Maria Joao Frade , I believe the
following is true:
Let $X$ be an infinite space with the cofinite topology, i.e.,
$U\subseteq X$ is open if and only if $U$ is empty or the complement
of $U$ is finite. This space is ${\bf T}_0$---${\bf T}_1$,
even---but it is not sober, since $X$ is irreducible closed, but $X$
is not the closure of any point. (You can make $X$ into a coherent
space by adding a generic point for $X$.)
$\Omega(X)$ is coherent. It is isomorphic to ${\rm Idl}(L)$, where
$L$ is the lattice of all $\{0,1}\}$-valued functions on $X$ that are
$1$ except at finitely many points.
J. Madden
Date: Tue, 11 Oct 1994 09:00:22 +0500 (GMT+4:00)
Subject: Graph-based Logic and Sketches
Date: 7 Oct 1994 19:30:41 GMT
From: Charles Wells
"Graph-based Logic and Sketches I: The General Framework" by
Atish Bagchi and Charles Wells is now available by anonymous FTP
from ftp.cwru.edu in the directory math/wells. It is also
available by gopher at gopher.cwru.edu, path
1/class/mans/math/pub/wells.
In either case the files are logstr.dvi and logstr.ps. To print
the dvi file requires AMS fraktur and the 1992 version of the
xypic fonts.
--
Charles Wells
Department of Mathematics, Case Western Reserve University
10900 Euclid Avenue, Cleveland, OH 44106-7058, USA
216 368 2893
Date: Fri, 14 Oct 1994 18:56:01 +0500 (GMT+4:00)
Subject: Lambda Definability in Categorical Models
Date: Tue, 11 Oct 1994 18:02:14 -0400
From: Andre Scedrov
A Characterization of Lambda Definability
in Categorical Models of Implicit Polymorphism
Moez Alimohamed
University of Pennsylvania
This paper contains the work of Moez Alimohamed, a mathematics graduate
student at the University of Pennsylvania who died tragically on August 29th.
Lambda definability is characterized in categorical models of simply typed
lambda calculus with type variables. A category-theoretic framework known
as glueing or sconing is used to extend the Jung-Tiuryn characterization of
lambda definability in Henkin models for the simply typed lambda calculus
first to ccc models, and then to categorical models of the calculus with
type variables.
WWW access is http://www.cis.upenn.edu/~andre/moez.html. The paper is also
available by anonymous ftp from the host ftp.cis.upenn.edu as the file
pub/papers/scedrov/def.ps.Z.
Date: Fri, 14 Oct 1994 18:58:19 +0500 (GMT+4:00)
Subject: literature on graphical algebras?
Date: Thu, 13 Oct 1994 10:23:33 +0100
From: Frank Piessens
Can somebody give me references to literature on Burroni's graphical
algebras? The only paper I know of is:
"Algebres graphiques" (A. Burroni), Cahiers de Topologie et Geometrie
Differentielle, XXII, 1981.
Many thanks,
Frank Piessens.
Frank.Piessens@cs.kuleuven.ac.be
Date: Sun, 16 Oct 1994 15:50:26 +0500 (GMT+4:00)
Subject: CT95: First Announcement
Date: Sun, 16 Oct 1994
From: Richard Wood
Please circulate to all interested colleagues:
FIRST ANNOUNCEMENT
INTERNATIONAL CATEGORY THEORY MEETING (CT95)
Canadian Mathematical Society Annual Seminar
July 9-15, 1995
Dalhousie University
Halifax, Canada
Fifty years after the paper which founded Category Theory and twenty-five
years after the discovery of Elementary Topos Theory, we are pleased to
invite the Category Theory community to meet next year in Halifax. The
meeting is also an Annual Seminar of the Canadian Mathematical Society
(which celebrates its 50th anniversary in 1995).
The conference arrival day is Sunday, July 9 and the scientific program
will run from Monday, July 10 to Saturday, July 15 inclusive.
Detailed information will be included in a second announcement. To
preregister, and thus receive subsequent announcements, please send
e-mail to ct95@cs.dal.ca with subject `preregistration'. Please provide
your name and a postal address in the body of the message.
If you do not have access to e-mail, you may write to:
RJ Wood, Chair
Local Organizing Committee, CT95
Mathematics, Statistics and Computing Science
Dalhousie University
Halifax, Nova Scotia B3H 3J5
CANADA
Date: Mon, 17 Oct 1994 10:48:59 +0500 (GMT+4:00)
Subject: Re: literature on graphical algebras?
Date: Mon, 17 Oct 1994 14:19:32 +0100 (BST)
From: Edmund Robinson
>
> Date: Thu, 13 Oct 1994 10:23:33 +0100
> From: Frank Piessens
>
>
> Can somebody give me references to literature on Burroni's graphical
> algebras? The only paper I know of is:
>
> "Algebres graphiques" (A. Burroni), Cahiers de Topologie et Geometrie
> Differentielle, XXII, 1981.
>
> Many thanks,
>
> Frank Piessens.
> Frank.Piessens@cs.kuleuven.ac.be
>
>
>
This is certainly the primary reference. Unfortunately there were problems
with Burroni's original proof that {toposes + logical morphisms} is
monadic over GRAPH. These are dealt with in
E.J. Dubuc and G.M. Kelly. "A presentation of topoi as algebraic relative to
categories or graphs", Journal of Algebra (81), 1983, 420-433.
There is also a certain amount of material on the example of toposes in
J. Lambek and P.J. Scott. "Introduction to Higher Order Categorical Logic",
CUP, 1986.
I suppose the main point of graphical algebras is that they give a syntax
for describing any category finitarily monadic over GRAPH as a category of
"algebras". A proof of that was known to Kelly at a quite early stage, but
can be recovered from the general machinery in
G.M. Kelly and A.J. Power. "Adjunctions whose units are coequalizers, and
presentations of finitary enriched monads", Jounal of Pure and Applied
Algebra 89 (1993), 163-179
There is also an account in my survey:
"Variations on Algebra: monadicity and generalisations of algebraic theories",
Sussex University Computer Science Technical Report 6/94, 1994.
all best wishes,
Edmund
Date: Mon, 17 Oct 1994 10:54:21 +0500 (GMT+4:00)
Subject: A query about quantales
Date: Mon, 17 Oct 1994 14:52:11 +0100 (BST)
From: Francois Lamarche
Has anyone every considered the following class of quantales? If * is
the tensor and I its unit, the additional axiom
u*v = I implies u=v=I
holds. If anybody has used them how are they called? Actually I am
interested in the ones among them that are also commutative and where I
is a dualizing element. In other words they are a specific class of
Girard quantales. There is an interesting subclass of them: look at
the following list of multiplication tables.
*| I 1 -1 *| I 1 0 -1 *| I 2 1 -1 -2
----------- -------------- ----------------
I| I 1 -1 I| I 1 0 -1 I| I 2 1 -1 -2
1| 1 1 -1 1| 1 1 0 -1 2| 2 2 1 -1 -2
-1|-1 -1 -1 0| 0 0 -1 -1 1| 1 1 1 -2 -2
-1|-1 -1 -1 -1 -1|-1 -1 -2 -2 -2
-2|-2 -2 -2 -2 -2
It is easy to see this generalizes for any set of the form
{ I, n,n-1,...,1,0,-1,...,-(n-1),-n } or
{ I, n,n-1,...,1, -1,...,-(n-1),-n }.
The slogan is "take the table for inf in the total ordering given by the
writing order and overwrite the lower right triangle with -n". The
dualizing operator is multiplication by -1 (keeping I fixed, natch). It
suffices to say what is the set of elements >= 1 to define the order on
the quantale, and it is always {n,I}. Thus the Hasse diagrams look like
1 1 2
| / \ / \
I 0 I 1 \
| \ / | I ...
-1 -1 -1 /
\ /
-2
This can be generalized even further: given a complete lattice with
an involution (-)~ : A^{op} -> A , on the set A+{I} define *
as follows:
/ a if b = I, ( b if a = I )
a*b = < bottom if a =< b~
\ a inf b if a not =< b~
Here as before the set of elements >= I is {top, I}
Have these ever been considered? Do they have a name?
Francois Lamarche
Date: Tue, 18 Oct 1994 23:15:16 +0500 (GMT+4:00)
Subject: new phone numbers for Sydney University
Date: Tue, 18 Oct 94 14:58:02 +1000
From: Max Kelly
Will colleagues please note that the prefix 692 has been changed to 351; thus
we have new university numbers:
Max Kelly +61-2-351-3796
Bob Walters +61-2-351-2966
Shu-Hao Sun +61-2-351-4076
Fax +61-2-351-4534
Regards from Max Kelly
Date: Tue, 18 Oct 1994 23:18:16 +0500 (GMT+4:00)
Subject: Re: literature on graphical algebras?
Date: Tue, 18 Oct 94 13:00:29 +0100
From: Pierre Ageron
----- Begin Included Message -----
Can somebody give me references to literature on Burroni's graphical
algebras? The only paper I know of is:
"Algebres graphiques" (A. Burroni), Cahiers de Topologie et Geometrie
Differentielle, XXII, 1981.
Many thanks,
Frank Piessens.
----- End Included Message -----
The subject of graphical algebras is highly interesting (to my taste !) but
rather controversial : there have been many mathematical misunderstandings and many
quarrels about who did what and when. Here are the main lines of my account of
the subject.
In my opinion the fundamental notion is that of an algebraic functor in the sense
of Coppey : this definition of algebricity is of a very intuitive and elementary
nature and is for me THE definition of algebricity. The corresponding framework was
introduced in [Coppey72] and is also described in [Coppey-Lair85]. An algebraic
functor need not have a left adjoint. In fact U is monadic iff U is algebraic and
has a left adjoint ! However an algebraic functor "with rank" is monadic. Now a
category of graphical algebras in the sense of Burroni is exactly a category C
with an algebraic functor C -> Graph. A controversial question (between Coppey
and Burroni !) is : are graphical algebras of any special importance ?
The only partial answer I can give is about the use of categories in computer
science : I have never seen any computer scientist make use of the fact that a
given type of structured categories (say c.c.c.'s) is algebraic over graphs. What
is really used is the algebraicity over "graphs with formal constructors" (some
kind of generalized sketches). The problem is that many sources that use that kind of
algebricity refer to Burroni's graphical algebras which is completely misleading :
for example the book [Lambek-Scott86] and the paper [Coquand-Ehrard87].
Categories with specified (co)limits of a given kind are algebraic over categories :
this is a classical result by Lair ([Lair75] or [Lair79]). In some cases
((co)products, (co)equalizers) they are also algebraic over graphs : see [Burroni81]
and [Coppey-Lair85]. Cartesian closed categories as well as elementary topoi are
also algebraic over graphs : the history of these results is not simple and
involves at least [Burroni81], [Dubuc-Kelly83], [MacDonald-Stone84] and [Ageron91].
An interesting example is that of Peano-Lawvere categories. It follows from general
reasons that they are algebraic over categories; Burroni raised the question : are they
algebraic over graphs - it was solved negatively in [Coppey-Lair85].
Much more could be said on that subject, e.g. the link between algebricity and
sketchability but this message is already too long. I refer to [Ageron91] for a
synthetic introduction and to [Coppey-Lair85] for more.
Pierre Ageron
References.
[Coppey72] Theories algebriques et extensions de prefaisceaux, Cahiers 13 (72) 3-40
[Coppey-Lair85] Algebricite, monadicite, esquissabilite et non-algebricite,
Diagrammes 13 (1985) 1-112
[Lambek-Scott86] Introduction to higher order categorical logic (Cambridge, 1986)
[Coquand-Ehrard87] An equational presentation of higher order logic, in LNCS 283
(Springer,1987)
[Lair75] Esquissabilite et triplabilite, Cahiers 16 (1975) 274-279
[Lair79] Condition syntaxique de triplabilite d'un foncteur algebrique esquisse,
Diagrammes 1 (1979) 1-16
[Dubuc-Kelly83] A presentation of topoi as algebraic relative to categories or
graphs, J. of A. 81 (1983) 420-433
[MacDonald-Stone84] Topoi over graphs, Cahiers 25 (1984) 51-62
[Ageron91] Structure des logiques et logique des structures, these, Universite
Paris 7, 1991, 196 pages
Date: Wed, 19 Oct 1994 16:01:23 +0500 (GMT+4:00)
Subject: coherent locales
Date: Wed, 19 Oct 1994 18:08:33 +0100 (MET)
From: Paul Johnson
Dear categories,
In ``Stone spaces'', Johnstone notes that the assumption that
every coherent locale is spatial is equivalent to the
prime ideal theorem for distributive lattices.
Is it generally agreed that the assumption that the spatial
part of every coherent locale has coherent topology is
also equivalent to the above two axioms?
Cheer, PBJ.
Date: Fri, 21 Oct 1994 12:36:58 +0500 (GMT+4:00)
Subject: colimits of Hilbert spaces
Date: Thu, 20 Oct 94 21:45:50 PDT
From: john baez
I'm interested in colimits in the category of Hilbert spaces
with isometries as morphisms. Is there a good reference on
when these exist?
John Baez
Date: Fri, 21 Oct 1994 12:35:36 +0500 (GMT+4:00)
Subject: Re: coherent locales
Date: Thu, 20 Oct 1994 16:46:15 +0100 (MET)
From: Paul Johnson
>
> Date: Wed, 19 Oct 1994 18:08:33 +0100 (MET)
> From: Paul Johnson
>
> Dear categories,
>
> In ``Stone spaces'', Johnstone notes that the assumption that
> (A) every coherent locale is spatial
>
> is equivalent to
>
> (B) the prime ideal theorem for distributive lattices.
>
> Is it generally agreed that the assumption that
>
> (C) the spatial part of every coherent locale has coherent topology
>
> is also equivalent to (A) and (B) above?
In a hopeless reply to my own querie,
it seems (after one sleepless night)
less and less likely that (C) ==> (B).
Ironically, since the trivial locale is coherent (and spatial),
for a coherent locale A to have a non-coherent spatial part,
it must have a point.
Conversely, axiom (C) still appears quite strong,
and I mean for tangible reasons:
For example, (C) holds iff the passage from coherent spaces
to distributive lattices has a left adjoint in coherent maps,
thus identifying what I would call the
``constructively-spatial'' distributive
lattices as reflective in all.
But might (C) hold without assuming any choice???
Apparently, most of this battle can be fought at the
level of Boolean algebras, but the reductions I have
yet to have sorted out.
Cheers, PBJ.
Date: Sat, 22 Oct 1994 11:28:54 +0500 (GMT+4:00)
Subject: Re: colimits of Hilbert spaces
Date: Fri, 21 Oct 94 12:23:33 EDT
From: Michael Barr
>
> Date: Thu, 20 Oct 94 21:45:50 PDT
> From: john baez
>
> I'm interested in colimits in the category of Hilbert spaces
> with isometries as morphisms. Is there a good reference on
> when these exist?
>
> John Baez
>
I don't know a reference, but I know that very few colimits exist.
For example, the sum of two non-zero spaces cannot exist for you can
give the direct sum of the normed spaces either the sup or euclidean
norm and these would both have to embed isometrically in the sum,
which is clearly impossible. Clearly coequalizers are likewise
precluded. It seems possible that filtered colimits might make it;
you would take the ordinary colimit as inner product spaces and
complete. I don't offhand see what can go wrong with that.
Michael
Date: Thu, 27 Oct 1994 16:14:55 +0500 (GMT+4:00)
Subject: sub-structures of free structures (
Date: Sun, 23 Oct 1994 15:35:43 +0000 (GMT)
From: "John G. Stell"
What results of the form `A sub-X of a free X is free' are known?
I am aware of groups, magmas (= set with binary operation), and
modules over a principal ideal domain. I'd be interested to hear of
structures for which this is either known to be true, or examples
where it fails.
John Stell
Date: Thu, 27 Oct 1994 18:16:28 +0500 (GMT+4:00)
Subject: PSSL in Aarhus
Date: Mon, 24 Oct 1994 14:01:41 +0100
From: Jaap van Oosten
This is an announcement of the 56th PSSL, to be held in the weekend of 3-4
December, in Aarhus, Denmark.
The announcement follows in Latex code. Please post this at your
department!
Jaap van Oosten
\documentstyle[12pt,a4]{article}
\pagestyle{empty}
\nofiles
\begin{document}
\begin{center}
{\Large\bf Announcement 56$^{\mbox{\small\bf th}}$ PSSL}
\end{center}
The 56$^{\mbox{\scriptsize th}}$ {\em Peripatetic Seminar on Sheaves and Logic}
will be held in the weekend of 3 and 4 December at the University of Aarhus, Denmark. As usual, we welcome talks on topics in logic, category theory
and related areas in mathematics and computer science. Please publicize this meeting amongst your colleagues.
At the time of the meeting, Ieke Moerdijk is in Aarhus as a guest of the
Mathematics Department.
The meeting will be jointly sponsored by the Mathematics department and the
research centre BRICS (Basic Research In Computer Science), so no fees are
to be expected.
There are two airports serving Aarhus: Tirstrup (Aarhus airport), which is
about 50 kilometres from the city and has a good bus connection to it, and
Billund, which lies about 100 kilometres from Aarhus and has connection by
bus (directly) or bus to Vejle and train from there (in some instances, the
latter connection is quicker). Further details, also about accomodation, will
follow. As we try to arrange relatively cheap accomodation in student houses,
it will be appreciated if attendants register as soon as possible.
\medskip
Return, preferably by email, to
\begin{tabbing}
aaaaaa\=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\=\kill
\> Jaap van Oosten, \> Tel.~++45-8942 3468\\
\> Datalogisk Afdeling, \> Fax ++45 8942 3255\\
\> Aarhus Universitet \> Email {\tt jvoosten@daimi.aau.dk} \\
\> Ny Munkegade, Bld.~540 \\
\> DK-8000 Aarhus C, Denmark
\end{tabbing}
We look forward to seeing you in Aarhus.\\
The local organizers,
\begin{quote}
\begin{tabbing}
Anders Kock\qquad\qquad\qquad \= Sergei Soloviev
\qquad\qquad \= Vladimiro Sassone\\
Claudio Hermida\> Jaap van Oosten
\end{tabbing}
\end{quote}
\hrule\vskip3pt
I would like to attend the 56th PSSL:\\ \\
Name\dotfill \\
Return Address\dotfill \\
\hbox{}\dotfill\\
email \dotfill \\
$\Box$ I wish to give a talk entitled \dotfill\\
of 20/30/45 minutes.\\
I wish to book accomodation from\dotfill to \dotfill \\
\end{document}
Date: Thu, 27 Oct 1994 18:24:30 +0500 (GMT+4:00)
Subject: ANNOUNCE: XY-pic version 2.12 released...
Date: Tue, 25 Oct 1994 13:17:10 +0100
From: kris@diku.dk
Dear category theorist,
This is to announce yet another BUG FIX release of my DIAGRAM DRAWING
PACKAGE, XY-pic: version 2.12. It fixes the following user visible
bugs in version 2.11:
* No conflict with `AMS-LaTeX' version 1.2 (SEE BELOW).
* No conflict with Karl Berry's `eplain' (SEE BELOW).
* Curves with explicit control are now right [Sjoerd Crans].
* Directional vectors no longer invalidate the Xy-state [Luc van Eycken].
* Tips on zero-sized turns no longer reversed [Jorge Almeida].
* Curves no longer overlap the surrounding text.
* Numerous documentation fixes in the Reference Manual.
* Short steep segments now placed correctly [thanks, Ross].
I am sorry to announce this very interim version which is necessary
because of a change in an internal function of AMS-LaTeX [sic]. Thus
** PLEASE UPDATE TO VERSION 2.12 IF YOU USE AMS-LaTeX ***
The release of the `real' version 3 (no longer in beta-test) is
imminent so you need not update otherwise unless any of the other bugs
have bothered you (or you desperately need one of the additions
described below).
There is ONE IMPORTANT CHANGE in the v3 extensions of this version:
the \arrow command has been renamed to \ar in order to make diagrams
more concise and avoid conflict with Karl Berry's `eplain', however,
using the `v2' compatibility option will still define \arrow (as well
as \stop and \merge that are also in conflict with existing names on
some systems).
- o -
One extension and one feature have been added with this release:
* \xyoption{cmtip} allows the use of arrow tips that resemble those
of D. Knuth's Computer Modern and Computer Concrete fonts.
* \xyoption{poly} supports drawing of regular polygons (by Ross Moore).
Version 3 will also have a special input mode for `knots and links'.
- o -
Xy-pic can be retrieved by anonymous ftp from
ftp.diku.dk : /diku/users/kris/TeX/
ftp.mpce.mq.edu.au : /pub/maths/TeX/
(see the README file as to the exact location below that), from
CTAN : /tex-archive/macros/generic/diagrams/xypic
and also through the World Wide Web (see below).
- o -
NEWS: there is now a World Wide Web HOME PAGE for Xy-pic in
which includes pointers to the sources as well as some TUTORIAL PAPERS
on Xy-pic:
* K.Rose: Xy-pic and Notation for Categorical Diagrams.
* R.Moore: Typesetting Neural Nets with Xy-pic.
(for people without WWW access these are also available on the ftp
servers in files xy/papers/ecct-94.ps and xy/papers/NeuralNets.ps).
- o -
In the hope that you will like the new things,
Kristoffer Rose
--
Kristoffer H{\o}gsbro ROSE
DIKU, Universitetsparken 1, 2100 K{\o}benhavn {\O}, DANMARK
Phones: +45 35321400 direct: +45 35321420 fax: +45 35321401
World Wide Web
Date: Fri, 28 Oct 1994 08:30:37 +0500 (GMT+4:00)
Subject: are local homemorphism part of a factorization system
Date: Thu, 27 Oct 94 16:27:20 +0100
From: Thomas Streicher
Does anyone know whether in the category Geom of toposes and
geometric morphism the local homemorphisms form the mono part of a
factorization system ?
Or is that at least the case in the luff subcategory where one has
only essential geomtric morphism whose leftmost adjoint preserves
pullbacks. Has this latter category ever been srudied ?
Thomas Streicher
Date: Fri, 28 Oct 1994 08:33:44 +0500 (GMT+4:00)
Subject: Re: sub-structures of free structures
Date: Thu, 27 Oct 94 18:24:26 EDT
From: Michael Barr
>
> Date: Sun, 23 Oct 1994 15:35:43 +0000 (GMT)
> From: "John G. Stell"
>
>
> What results of the form `A sub-X of a free X is free' are known?
> I am aware of groups, magmas (= set with binary operation), and
> modules over a principal ideal domain. I'd be interested to hear of
> structures for which this is either known to be true, or examples
> where it fails.
>
> John Stell
>
It is true for abelian groups, but is false for both monoids and
commutative monoids. The free (commutative) monoid on one element x
has a submonoid consisting of 1,x^3,x^5,x^6 and all x^n for n > 7
is not free. Throwing away 1, you get counter-examples for
semigroups and commutative semigroups. By taking the free abelian
group on this example, you get counter-examples for rings and
commutative rings. I am sure that it is a fairly rare occurrence.
Michael Barr
Date: Fri, 28 Oct 1994 08:27:54 +0500 (GMT+4:00)
Subject: are local homemorphism part of a factorization system
Date: Thu, 27 Oct 94 16:27:20 +0100
From: Thomas Streicher
Does anyone know whether in the category Geom of toposes and
geometric morphism the local homemorphisms form the mono part of a
factorization system ?
Or is that at least the case in the luff subcategory where one has
only essential geomtric morphism whose leftmost adjoint preserves
pullbacks. Has this latter category ever been srudied ?
Thomas Streicher
Date: Mon, 31 Oct 1994 11:12:33 +0400 (GMT+4:00)
Subject: Re: sub-structures of free structures
Date: Sat, 29 Oct 1994 13:02:47 -0400 (EDT)
From: MTHISBEL@ubvms.cc.buffalo.edu
There is certainly a good bit more known than in Michael's response. The
varieties in which subalgebras of free algebras are free are called Schreier
varieties. A paper of mine in the early 70's -- Epimorphisms and dominions, V,
probably in Alg. Univ. -- answered someone's question (Sabbagh?): Is every
Schreier variety balanced? I remember the answer was No. John Isbell
Date: Mon, 31 Oct 1994 11:07:12 +0400 (GMT+4:00)
Subject: Re: sub-structures of free structures
Date: Fri, 28 Oct 1994 10:58:22 -0400
From: Peter Freyd
John Stell asked when to expect subobjects of free objects to be free
and observed that such is the case for modules over prinicpal ideal
domains. For commutative rings that's the only case: if every ideal is
free as a module then the ring is a PID.
He points out that subalgebras of free algebras are free if the theory
consists of just one binary operation and no equations. Isn't that the
case for any equationless theory?