Subj:	ftp paper
Date: Wed, 12 Aug 92 14:47:57 EDT
From: cubric@triples.Math.McGill.CA (Djordje Cubric)

I would like to announce that the draft of my paper "On Free CCC" 
is available from ftp triples.math.mcgill.ca. The paper contains a
proof of the following:

Theorem: Let C be a free cartesian closed category. Then there exists a
faithful structure preserving functor F:C->Set.

Isn't this just the H. Friedman's completeness result for the typed
lambda calculus? NO. One has also to show that in the free cartesian
closed category  all the  arrows into the terminal object are epi. 
 
We prove the result using Mints' reductions (but with a repaired proof). 
Along the way we conclude also that:

Mints reductions are weakly normalizing, the strategy being: first do
all eta-like expansions (with the restrictions) and
then beta-like reductions.  

To get the file (if you can read ps files) do:
ftp triples.math.mcgill.ca
Name: anonymous
Password: "your e-mail address"
>cd pub/cubric
>binary
>get frccc.ps
>quit

If you can't read ps files there are also frccc.dvi and frccc.tex (which needs
Barr's diagram.tex macros and they are at the same ftp site except under
pub/texmacros). In case of any problems I'll gladly send you a copy by
regular mail. Any comments are welcome.
Djordje Cubric


==============================================================================
Subj:	October Meeting
Date: Thu, 13 Aug 92 08:30:51 EDT
From: fox@triples.Math.McGill.CA (Thomas F. Fox)

CATEGORY THEORY MEETING:  OCT 10-11, 1992
 
CATEGORY THEORY RESEARCH CENTER, MCGILL UNIVERSITY, MONTREAL
 
Dear Colleague,
 
     We look forward to seeing you again this fall.  We will meet 
in the basement of Burnside Hall (805 Sherbrooke St W) at 9:00
Saturday morning for coffee, and the first talk will be at 9:30.
If you wish to speak, please contact Michael Barr as soon as possible.
A final list of speakers will be drawn up Saturday morning.
 
     Below you will find a list of hotels and tourist rooms within
easy walking distance of McGill.  You should mention McGill when
making your reservation to obtain the quoted price.  If you have any
further questions, contact Tom Fox.

                          Hotels:
L'Appartement, 455 Sherbrooke W, 284-3634, $82.50
Howard Johnson Plaza, 475 Sherbrooke W, 842-3961, $79
Citadelle, 410 Sherbrooke W, 844-8851, $84.50
Delta, 475 President Kennedy, 289-1986, $89
Four Seasons, 1050 Sherbrooke W, 284-1110, $140
Holiday Inn, 420 Sherbrooke W, 842-6111, $94
Journey's End, 3440 Park Ave, 849-1413, $75-85
Hotel du Parc, 3625 Park Ave, 288-6666, $90
Versailles*, 1659 Sherbrooke W, 933-3611, $89

               Tourist Rooms:
Ambrose, 3422 Stanley, 288-6922, $45-50
Armor*, 151 Sherbrooke E, 285-0140, $32-59
Casa Bella, 258 Sherbrooke W, 849-2777, $39-75
Pierre*, 169 Sherbrooke E, 288-8519, $35-55
 
*20 minute walk from McGill
 
Michael Barr  barr@triples.math.mcgill.ca
Tom Fox       fox@triples.math.mcgill.ca
==============================================================================
Subj:	Geometric or coherent logic?
Date: Tue, 18 Aug 92 16:04:15
From: sjv (Steve Vickers)@doc.ic.ac.uk

I've become accustomed to referring to -

- coherent logic, with connectives true, /\, false, \/, = and (exists); and
- geometric logic that also admits infinitary \/.

I think I got this sense of "geometric" from Mike Fourman, and then 
"coherent" is natural because coherent theories are classified by coherent 
toposes. But the published works vary considerably. In particular,

where I have               coherent                geometric,

Makkai and Reyes have      finitary coherent       coherent,
Johnstone has              finitary geometric      generalized geometric
MacLane and Moerdijk have  geometric               (not referred to).

Is usage as chaotic as it appears?

Steve Vickers.
==============================================================================
Subj:	From Jurgen Koslowski
Date: Wed, 19 Aug 92 16:16:37 CDT
From: koslowj@math.ksu.edu (Juergen Koslowski)

The time seems to have come to bid farewell to the mathematics
community as a whole, and to category theorists in particular. It has
been a privilege for the last 10 years to be able to work in this very
special area of mathematics.

Although I did receive a last minute job offer earlier this month from
an U.S. University, after agonizing negotiations the terms of this
offer turned out to be insufficient to procced with an application for
the "green card". After having had an H-1 visa for 6 years, a further
extension was not possible either. My present H-1 visa expires on
August 31, which gives me until the end of September (I guess) to
leave the U.S. and return to Germany.

If anybody knows of a position that might be available on (very) short 
notice, please contact me immediately by email

	koslowj@math.ksu.edu   or   koslowj@cis.ksu.edu

A position in the U.S. would have to be a "tenured or tenure track or
a permanent research position". 

If I am forced to move back to Germany I will post a mailing address.
I would appreciate it if you could keep me on your mailing lists for
pre-prints, although at the moment I do not know whether I can stay
involved in mathematics professionally. 

Thank you all very much for making these last 10 years worthwhile!

-- J"urgen Koslowski
==============================================================================
Subj:	Geometric or coherent logic?
Date:        Sun, 23 Aug 92 22:28:46 EDT
From:        MT78000 <MT78%MUSICA.MCGILL.CA@VM1.MCGILL.CA>

This is Michael Makkai replying to Steve Vickers' query on coherent
vs geometric logic. Despite the variety you found in the literature,
I think you are right about the standard usage. I certainly have used
the terms in those senses now for a long time (despite what appears in
Makkai/Reyes). I think Andy Pitts will agree with me; in fact I vaguely
recall that I told myself at one point that I would observe Pitts'
usage in this respect.
==============================================================================
Subj:	Linear Algebra
Date: Fri, 21 Aug 92 23:34:37 +0200
From: Magne.Haveraaen@ii.uib.no (Magne Haveraaen)

Can anyone help me with accessible (in both senses of the word) references
to algebraic (as in many-sorted algebraic specifications) or category
theoretic definitions of linear algebra (real numbers, vector space,
Banach space, Hilbert space, tensors, manifolds, etc.). Most books on
linear algebra do this to some extent, but, after establishing the
isomorphism between matrices and homomorphisms over vector spaces, the
rest of the exposition is done in terms of the matrix representation.
This is especially true for the area of tensors, which has developed its
own peculiar notation.

Magne

Magne Haveraaen			e-mail:	magne@ii.uib.no
Dept. of Informatics		phone:	+47 (5) 544154
University of Bergen		fax:	+47 (5) 544199
Hoyteknologisenteret
N-5020 BERGEN
Norway
==============================================================================
Subj:	Yoneda
Date: 19 Aug 92   13:11:03 EST
From: <cxm7@pop.cwru.edu>

-------------

	While we are asking terminological questions prompted by Mac Lane
and Moerdijk, I'd like to know exactly what people mean by the
Yoneda lemma.  Does Yoneda include the fact that every presheaf is
a canonical limit of representables?  Does it include (as Johnstone 
has it, on _Topos Theory_ p.51) the claim that the Yoneda embedding to 
a presheaf category is left adjoint to the forgetful functor (i.e. 
the functor that forgets the action of arrows and only remembers the 
family of sets indexed over the objects of the domain category)?

Colin McLarty 

==============================================================================
Subj:	The square brackets notation for denotation
Date: 26 Aug 92   08:42:15 EDT
From: Charles Wells <cfw2@po.cwru.edu>


Topos theorists and people in denotational semantics use the
notation [[t]] to denote a mathematical object that is the
meaning of t in some semantics.  In particular, in the case of a
formula f, [[f]] is the truth value.  APL and Donald Knuth use [f]
for the truth value of a formula (or so I have been told).  Does
anyone know who used the double square bracket notation first
(topos theorists, denotational semantics people, or whoever),
and whether it was suggested by the APL usage?

--
Charles Wells
Department of Mathematics, Case Western Reserve University
University Circle, Cleveland, OH 44106-7058, USA
216 368 2893

==============================================================================
Subj:	4 colours
Date: Tue, 25 Aug 92 15:18:46 EDT
From: pavlovic@triples.Math.McGill.CA (Dusko Pavlovic)

A note describing

	A CATEGORICAL SETTING FOR THE 4-COLOUR THEOREM
	by Dusko Pavlovic

is available by anonymous ftp.

	Abstract:

It is well known that the 4-colouring of maps is equivalent to the
3-colouring of the edges of some graphs. We show that every slice of
the category of 3-coloured graphs is a topos.  The forgetful functor
to the category of graphs is cotripleable; every loop-free graph is
covered by a 3-coloured one in a universal way. In this context, the
4-Color Theorem becomes a statement about the existence of coalgebra
structure on graphs.

The "projective" approach to graphs, described here, is, in a sense,
dual to the usual combinatorial treatment, based on induction. I shall
try to relate the two approaches in another paper.

	
	How to get a copy:

>ftp triples.math.mcgill.ca
>login: anonymous
>password:[your e-mail address]
>cd pub/pavlovic
>bin
>get 4color-US.ps.Z	%if your printer has American standards
	%or
>get 4color-A4.ps.Z	%otherwise
>bye
>uncompress 4color-++.ps.Z

If you have any problems printing out this PS-file, please let me
know. (I am not distributing the DVI or LaTeX versions of the paper
because it contains several PS-diagrams.)

	Regards,
	Dusko

==============================================================================
Subj:	Re: Yoneda
Date: Mon, 31 Aug 92 10:28:52 EDT
From: pjf@saul.cis.upenn.edu (Peter Freyd)

In the phrase "Yoneda lemma" the first word is generic.  The connection
with Yoneda is as follows.  I wrote a letter to David Buchsbaum in
1959 in which I used one of the lemmas now known as Yoneda's.  (I had
seen the lemma in an abstract in the Notices by Watts.)  Barry Mitchell,
in a return letter, mentioned that the lemma was Yoneda's.  In the
book Abelian Categories I give a reference to a paper by Yoneda for
the lemma.

Some years after the publication of the book a student complained to
me that the lemma does not appear in the cited paper.  The complaint was
duly passed on to Barry.  He refered to his notes from the lectures
that Mac Lane had given in the summer of 58 or 59 (I think) on Yoneda's
treatment of the Ext functors, in which notes the lemma does appear.
Barry had assumed that the lemma was in the paper that Saunders was
reporting on.  And, of course, I never thought of actually looking
at a paper I was citing.

But Yoneda must have known the Yoneda lemma.  One may describe the
Yoneda lemma as case zero of his theorems on Ext.  The lemma certainly
needs a name and Yoneda sounds nice.

In that original formulation it is just the lemma that the maps from
a functor represented by an object, A, to an arbitrary set-valued 
functor, F, are in natural corespondence with the elements of  F(A).
(Well, not quite: the original formulation was for additive categories
and instead of "set-valued" it was "group-valued".)

Almost immediately the phrase was generalized.  I remember John Gray
in the early 60's talking about the importance of the Yoneda lemma 
in enriched category settings.

I don't know what Yoneda has to say about all of this.  If he had stayed
in pure mathematics he probably would have proved too many things to make
the name useful as the sole description of a single lemma.  As it is,
though, the name serves well.


++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Date: Mon, 31 Aug 92 11:10:01 EDT
From: barr@triples.Math.McGill.CA (Michael Barr)

As far as I am concerned the Yoneda is either the statement that
NT(Hom(A,-),F) iso FA
(naturally in A and F) of else the special case when F is also
representable.  The latter is probably the way Yoneda stated it.  The
rest is the Grothendieck construction or something.  

Michael
==============================================================================
Subj:	Re: Yoneda
Date: Mon, 31 Aug 92 14:17:08 EDT
From: barr@triples.Math.McGill.CA (Michael Barr)

Peter's comments on the Yoneda lemma are interesting.  Phil Scott was
in Japan some years ago and actually spoke to Yoneda and it would be
interesting to hear what he has to say.  

Computer scientists are fascinated by the fact that I actually know
Kleisli and that he is still around.  And that he actually did do the
Kleisli construction.

Michael
==============================================================================
Subj:	Re: square brackets
Date: Mon, 31 Aug 92 09:34:02 +0100
From: Mike Fourman <mikef@dcs.ed.ac.uk>

> From: Charles Wells <cfw2@po.cwru.edu>

> Topos theorists and people in denotational semantics use the
> notation [[t]] to denote a mathematical object that is the
> meaning of t in some semantics.  In particular, in the case of a
> formula f, [[f]] is the truth value.  APL and Donald Knuth use [f]
> for the truth value of a formula (or so I have been told).  Does
> anyone know who used the double square bracket notation first
> (topos theorists, denotational semantics people, or whoever),
> and whether it was suggested by the APL usage?


The first occurrence I know of is in the Scott-Solovay
treatment of Boolean-Valued models. I've always called them
"Scott-open and Scott-close".

Mike

Prof. Michael P. Fourman                     email        mikef@dcs.ed.ac.uk
Dept. of Computer Science                    'PHONE (+44) (0)31-650 5198 (sec)
JCMB, King's Buildings, Mayfield Road,              (+44) (0)31-650 5197
Edinburgh EH9 3JZ, Scotland, UK                 FAX (+44) (0)31 667 7209

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Date: Mon, 31 Aug 92 09:34:24 BST
From: Robert Tennent <rdt@dcs.ed.ac.uk>

My guess is that logicians used it long before any of these did,
and that the origin is that it evolved from parenthesized
Quine corners:   _        _
               (|  syntax  |)

Bob Tennent

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Date: Mon, 31 Aug 1992 14:48:23 +0200
From: F.J.de.Vries@cwi.nl

At least in 1975 Scott, Strachey and Stoy used such [[..]] notation,
but it should be possible to go beyond that, as you do yourself
perhaps with the reference to Knuth and APL.

The question intrigued me because my reflex was to believe that the
notiation should come from good old model theory. But that seems not
be the case.

Fer-Jan de Vries,
CWI, Amsterdam.

++++++++++++++++++++++++++++++++++++++++++++++++++++

Date: Mon, 31 Aug 92 10:23:03 EDT
From: pavlovic@triples.Math.McGill.CA (Dusko Pavlovic)

Some people call the double square brackets SCOTT BRACKETS.
Could it be that Dana Scott first used them in 1967, in his
notes on Boolean-valued models of set theory?
	Dusko Pavlovic

+++++++++++++++++++++++++++++++++++++++++++++++++++++
Date:        Mon, 31 Aug 92 14:26:27 ADT
From: dbenson@yoda.eecs.wsu.edu (David B. Benson)

The first place I encountered this notation is

Joseph E. Stoy
Denotational Semanatics:
		The Scott-Strachey Approach to Programming Langauge theory
The MIT Press, 1977

I quote from page 29:
	The brackets [[ ]], used round an argument of a semantic function,
	always enclose expressions in the object langauge, possibly
	including metalanguage variables.
There appears to be no discussion of the history, other than Stoy perfers
this to Quine's quasi-quotes (Quine's corners)

Unfortunately, this book is, I believe, out-of-print.

Regards to all,
David

==============================================================================
Subj:	Yoneda and square brackets
Date: Mon, 31 Aug 92 16:45:01 EDT
From: es@math.mcgill.ca (Elaine Swan)


To the best of my knowledge, the observation
that every presheaf is a canonical limit of representables
first appeared in ``Completions of categories'',
Springer LNM 24 (1966). The double square brackets
are usually associated with Dana Scott,

Jim Lambek
==============================================================================
Subject: Online LICS bibliography
From: dmjones@theory.lcs.mit.edu (David M. Jones)
Date: Mon, 31 Aug 92 16:52:54 EDT

The online bibliography for the Annual IEEE Symposium on Logic in Computer
Science has now been updated to include all of the papers published in the
proceedings of the Seventh meeting, which took place in June 1992.  The
bibliography contains abstracts for all of the papers from the 1992
meeting.

The bibliography, which is in BibTeX format, is available via anonymous ftp
and mail server from theory.lcs.mit.edu [18.52.0.92] in the file
pub/meyer/lics.bib.

To retrieve the file via ftp, connect to theory using "anonymous" as the
login name and "guest" as the password.

To retrieve the file via mail server, send a message to the address
archive-server@theory.lcs.mit.edu with the following line in the body:

        send meyer lics.bib

An index of other available files can be retrieved with the command

        send meyer Index

More information on the archive-server can be obtained by sending a message
with only the word "help" in the body.

David M. Jones
MIT Lab for Computer Science
Administrator, {types,logic,concurrency}@theory.lcs.mit.edu


