Date: Fri, 6 Jan 1995 23:12:19 -0400 (AST)
Subject: 1. ctrc.html 2. Tensor and Linear Time

Date: Fri, 6 Jan 1995 16:52:40 -0500
From: Jim Otto <otto@rodent.math.mcgill.ca>

Dear People

1.  There is now a small web page at URL

        ftp://triples.math.mcgill.ca/ctrc.html

for the Centre de Recherche en Th'eorie des Cat'egories -- Montr'eal.

2.  Linked to that web page is my web page and linked to my web page
is an expanded and corrected paper on linear time, whose introduction
is below.

Bon Jour, J. Otto

                        Tensor and Linear Time

Introduction

Quite simply, serial composition is

        <---   <---

while parallel composition = tensor is

        <---

        <---

even though we will run both sequentially (section 4.6).  Tensor,
rather than product, not only provides more models [Huwig 82], but may
be necessary at tier 0 in order to avoid the diagonal bug (section
4.6).  Roughly, tier 0 is what may go inside loops, while tier 1 is
what is defined by loops (section 4.1).  By the way, 0-ary serial
composition = the identities, while 0-ary parallel composition = the
unit.

The main text consists of sections 1. Almost Equational Specification,
2. Tensor and System T, 3. Comprehensions and Tiers, 4. Linear Time,
and 5. The Linear Time Hierarchy.  Section 4 characterizes the linear
time functions, using ideas from [Bellantoni-Cook 92, Bloch 92,
Leivant-Marion 92], and provides a formal system for them.  Section 5
characterizes, improving [Wrathall 78], the linear time hierarchy
relations. (These are the Delta_0 relations [H'ajek-Pudl'ak 93, Woods
86].)  Section 1, using ideas from [Makkai 94, Ad'amek-Rosick'y 94],
explains the almost equational specification which we use throughout.
It is based on 2 layers of restricted equational specification:
sketches and orthogonality.  Section 2 specifies the idealized, but
unfeasible, recursion of G"odel's system T, while section 3 provides a
means, namely comprehensions and tiers, to attain feasibility.
Technical issues have been pushed to the appendices, which are
A. Sketches as Presheaves, B. Initial Models, C. Coherence, D. Linear
Implication, E. Cotensor, F. Gluing, and G. Turing machines.  The main
text is hopefully generally readable with perhaps a few glances at say
[Barr-Wells 90, 85].

We have used latex2e, xy-pic, and auc-tex.

Date: Tue, 10 Jan 1995 00:27:14 -0400 (AST)
Subject: Tools for cat theory: Using ftp rather than mosaic.

Date: Mon, 9 Jan 1995 11:17:48 -0500
From: Jim Otto <otto@rodent.math.mcgill.ca>
To: stone@math.ubc.ca


     Hi.  Coming in using ftp I don't find anything I can "get"
   (that seems to be related to your Tensor and Linear Time paper.)
   Perhaps I should learn something about "crtc.html".  Can you
   suggest what command I should begin with (using what's essentially
   BSD 4.3 on a dept. NeXT to which I'm connected via modem and phone
   line ((to another NeXT on my desk)) ) ?  I've been trying
   "appropos" with everything I can think of, like "ctrc" and "html",
   but so far with no hits.  Art

Dear Art Stone

So my directions on

<li> <a href=ftp://triples.math.mcgill.ca/ctrc.html>
Centre de Recherche en Thiorie des Catigories --
Montrial.</a>

were too implicit.  To use ftp rather than say mosaic

1.  Do anonymous ftp to triples.math.mcgill.ca

2.  get ctrc.html

By the way, it's not according to the French spelling or the Canadian
version of the American FCC, but rather the English spelling `Category
Theory Research Center'.

3.  Read that J. Otto is at pub/otto/otto.html

<li> <a href="pub/otto/otto.html"> J. Otto</a>

4.  cd pub/otto and then get otto.html

5.  Read that the new paper is at c-docs/tensor.ps.gz

New papers on complexity doctrines.
<ul>
<li> <a href="c-docs/tensor.ps.gz">
Tensor and Liner Time</a> (42 pages).  Submitted to the proceedings of
the workshop on logic and computational complexity.
</ul>

6.  cd c-docs and get tensor.ps.gz

7.  If you don't have gunzip, get it from say the GNU directory on
gatekeeper as pointed to by otto.html.

<li> <a href=http://gatekeeper.dec.com:80/pub/>
Gatekeeper.</a>

Well actually that one won't work for ftp.  This one will

<li> <a href=ftp://gatekeeper.dec.com/pub/>
GNU</a>

Or get someone to setup a web previewer, say mosaic, and its
utilities, especially gunzip, gs, and ghostview.  O'Reilly has a nice
book on mosaic.

<li> <a href=http://nearnet.gnn.com/bus/ora/index.html>
O'Reilly & Associates, Inc.</a>

So, just as .bib's are useful even without bibtex, .html's are useful
without mosaic, lynx, or WWW.  On the other hand, newer software can
make guru mumbo jumbo a no-brainer.

Bon Jour, J. Otto


Date: Mon, 6 Oct 1997 09:15:28 -0300 (ADT)
Subject: Montreal Category group new WWW address (URL) 

Date: Sun, 5 Oct 1997 16:54:24 GMT
From: Robert A. G. Seely <rags@triples.math.mcgill.ca>


Triples has been down for a while, especially its ftp interface
with the outside world. Things seem to be back to normal again.
So if you have had trouble getting papers from our ftp site, 
please try again - things ought to be working.  (And please
let us know if you still have trouble.)

One thing has changed: we have a simpler WWW URL for the group's
home page.  The old URL still works, but you might want to update
any links you have to the new one:
  http://triples.math.mcgill.ca
(Individual team members may or may not also change their WWW
page URLs, but at present, only the old ones are active, so don't
try to "guess" other URLs based on the team one.  There are links
to all the team members WWW pages or ftp sites on the group page.)

= rags =



Date: Wed, 17 Dec 1997 13:53:22 -0400 (AST)
Subject: Triples down etc 

Date: Mon, 15 Dec 1997 10:48:12 -0500 (EST)
From: Robert Seely <rags@scylla.math.mcgill.ca>

Bob - we have had more troubles with triples, and it is down and out for
the time being.  Can you please make appropriate adjustments to the
categories list, and perhaps post this message to the list as well?  All
email addresses with "triples" in them ought to just have the "triples"
dropped, so, eg, barr@triples.math.mcgill.ca would become
barr@math.mcgill.ca, and similarly (for example) for bunge, fox, hermida,
lambek, makkai, rags, ruet.  The aliasing system we had on triples for the
category community is of course not functioning. If there are any problems
with email, get in touch with me (rags) or barr (@math.mcgill.ca) and
we'll see what can be done.

FTP and HTTP url's with "triples" in them will also not work, of course.
Some of us have home pages on other machines in the maths dept - those
will still function.  Our papers are mirrored by Hypatia, so one should
check out that site for most purposes.  (There is a link on my www page,
listed below, if you don't know how to get there.)  

We hope this problem will be short-lived, bear with us in the meantime.

best regards, Robert

===========================
RAG Seely
<rags@math.mcgill.ca>
<http://www.math.mcgill.ca>
===========================


Date: Fri, 18 Sep 1998 10:16:57 -0400 (EDT)
From: Michael Barr <barr@triples.math.mcgill.ca>
Subject: categories: ftp on triples

We have apparently had some kind of break-in on triples using the ftp
demon.  The only damage has been the downloading of enormous quantities of
material.  Enough to slow triples to a halt and also to get the computing
centre upset enough to threaten to remove us from their net.  Therefore,
we have disabled anonymous ftp.  I am now trying to find out if the
material is available from the web and, if not, how to make it available.
In any case, if there is something you need, please write and ask the
author and s/he will undertake to email it to you.

Later on, we will decide what to do.  One possibility is to password
protect it and announce the password on this list.  This will protect us
from random browsers, while leaving it available to all subscribers to
this list.

Michael


Date: Mon, 21 Sep 1998 14:49:51 -0400 (EDT)
From: Michael Barr <barr@triples.math.mcgill.ca>
Subject: categories: ftp on triples

I did not go into details on the problems we had, but so many have written
to me offering diagnoses incompatible with the facts that I figure it is
easier to describe them once and for all.  There were two symptoms.  First
triples essentially stalled for minutes at a time.  More seriously, the
computer centre made a formal complaint that triples was generating so
much traffic that it was seriously compromising the internet connection.
Since McGill is the gateway to all of Quebec, this is serious business.
There was an implicit threat to cut the department off if we didn't do
something about it.  I suppose then the department could have cut triples
off, although it never went that far, since I first tried changing the
root password in case whoever it was was changing the logs.  This had no
effect and the logs left little doubt that the only oddity was the ftp
signons which showed simultaneous (maybe 8-10) from the same origin and
that not identifiable by nslookup.  (This last fact is not, in itself
suspicious; the machine I am now using gets a new IP address whenever it
is booted and cannot be identified by nslookup.)  But the machine that
does this is different every time.  So it cannot be explained by,
according to one suggestion, some newbie getting confused and copying the
same thing many times.  In fact, it is hard to know how you could copy
enough to fill the while I-net channel.  At any rate, closing the ftp
access seems to have cured it.  We are mulling over what to do.  Some
think that putting a password will inhibit non-category theorists that do
not subscribe to the list.  And I guess it would compromise Hypatia.  But
I think Vaughan mirrors triples anyway.

Michael


Date: Wed, 23 Sep 1998 01:09:15 -0400 (EDT)
From: "R.A.G. Seely" <rags@math.mcgill.ca>
Subject: categories: URL update for Category group, Montreal (Lambek Festschrift, etc)

Recently there have been some security problems with the Montreal
Category Group's ftp site on triples.  This seems a good opportunity
to remind people that our old "ftp-based" URLs have been updated for
WWW use.  In particularly, the "official" URL for the group's WWW page
is (and has been for a while now)

      http://triples.math.mcgill.ca

(note the absence of the redundant "www" prefix)

Related URLs that are linked to this include the recent call for
papers for the Lambek Festschrift (deadline 31 Jan 1999)

     http://triples.math.mcgill.ca/lambek/LambekVol.html

as well as the current seminars of the group, and the table of
contents for the upcoming special issue of JPAA in honour of Mike Barr
("Barrfest").

     http://triples.math.mcgill.ca/~rags/seminar/
     http://triples.math.mcgill.ca/barrfest/bfpapers.html

(and other links of interest...)

The last time a note such as this went out, we promised to support the
"old" urls for a time - that time may be running out now, so we
encourage all interested to verify that your links and bookmarks are
up-to-date in this regard.  For the time being, any ftp to triples may
be unreliable, until the security issues are resolved.

= rags =
(Robert Seely)

<rags@math.mcgill.ca>
<http://www.math.mcgill.ca/~rags>


Date: Wed, 7 Oct 1998 15:08:05 -0400 (EDT)
From: Michael Barr <barr@triples.math.mcgill.ca>
Subject: categories: ftp site

From now on, all the ftp sites here have been amalgamated to
ftp.math.mcgill.ca.  The material from triples, and a couple of other
servers, have been amalgamated, but my papers are still found in pub/barr
and Seely's in /pub/rags and so on.  In a few days, you will be informed
of this site if you try to sign on anonymously to triples.

Sorry for the interruption.

Michael


Date: Tue, 1 Dec 1998 13:50:21 -0500
From: Michael Barr <barr@math.mcgill.ca>
Subject: categories: triples down

The subject says it all.  In general, you should ALWAYS use the address
barr@math.mcgill.ca since I can adjust that for the viccissitudes of
computerdom.

What is happening is that someone is getting into it and sending out gobs
of material, enough to generate official complaints from downstream
computers and the CC here has turned it off.  This happened last summer
and we assumed it was ftp, but now we have turned that off, as most of you
know.  To make matters worse, our technician is a student.  We moved the
computer to the computer centre last summer because our offices had no air
conditioning and the CC absolutely will not permit students to enter for
any reason whatever.  I guess we will have to take it out.


Date: Mon, 28 Dec 1998 11:32:17 -0500 (EST)
From: "R.A.G. Seely" <rags@math.mcgill.ca>
Subject: categories: Mail to McGill not functionning

It may be of relevance to some on this list to know that for the past
week, the main machine in the maths dept at McGill has not been
functionning, and so, as a consequence, mail sent to
"user@math.mcgill.ca" will not have been received.  Triples *is*
functionning, so although usually the generic address as above is
preferred, you might try cc'ing any mail you have sent to
"user@triples.math.mcgill.ca" - for those of us that still use
triples, this will get through.  We'll let you know when things are
back to normal - this has been delayed by the holidays, of course.

= rags =

PS - The categories home page <http://triples.math.mcgill.ca> is still
functionning, which has information about the Lambekfest (call for
papers), the Barrfest (table of contents), and current seminars.
Links on that page to members' home pages may not function, if they
are links to the main departmental machine, however.  (You'll get the
idea from my (revised) sig below...)

=================================
<rags@math.mcgill.ca> (currently not functionnal)
<rags@triples.math.mcgill.ca> (still OK)
<http://www.math.mcgill.ca/~rags> (currently not functionnal)
<http://triples.math.mcgill.ca/~rags> (still OK)


Date: Tue, 24 Aug 1999 18:23:05 -0400 (EDT)
From: "R.A.G. Seely" <rags@math.mcgill.ca>
Subject: categories: HTML at McGill Maths Dept

Some of you may have experienced difficulties getting to web pages on
triples lately.  There have been security problems at McGill of late,
and all "access" from the outside is being severely limited.  For the
time being (and perhaps permanently), all urls of the form
   http://triples.math.mcgill.ca/<whatever>
can be accessed using the form
   http://www.math.mcgill.ca/triples/<whatever>

In particular, the Category center page is now 
   http://www.math.mcgill.ca/triples

The "www.math.mcgill.ca/triples" format will probably become
permanent, but we hope to have the older "triples.math.mcgill.ca"
format operational again soon (so old bookmarks and links will
function again).  We shall see...

 - all the best, Robert 

PS:
We are trying to find a method that will make the above translation
automatically, without user intervention, and (here is the hard bit)
without any actual access to an http server on triples.  If you have
any technical comments on how to do this (or if it is indeed
impossible), let us know please.


=================================
rags@math.mcgill.ca
http://www.math.mcgill.ca/~rags