
Date:        Sat, 08 Sep 90 14:27:53 EDT
From:        Michael Barr <INHB@MUSICB.MCGILL.CA>

                         Category Theory, 1991
                23--30 July, McGill University, Montreal
            Groupe Interuniversitaire en Etudes Categoriques

                     Request for financial support

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We will have a limited amount of funds to support people who cannot
attend without such support.  It will be MUCH easier to fund
people who require only housing and food than people who also require
transportation.  In particular, people from eastern Europe and the
Soviet Union will be expected to try to arrange transit on their own
national airline.  Other people are well advised to try the Canadian
airline Nationair which seems to have the cheapest fares we have seen.
Because of present uncertainties, it may be difficult to get firm
prices, but you will have to try to get an estimate if you wish to ask
us for travel funds.  People who do not request travel funds will have a
much better chance of being funded for food and housing.

Owing to the exigiencies of the funding organization, we must have your
request, including a title for your talk, as soon as possible and no
later than October 5.  If you receive this by Email you will not get it
by post.  Please reply the same way.  If you receive it by post and can
reply by Email, please do so, giving the same information.

We will then need an abstract by March 15, 1991 and will be attempting
to announce the amounts we can provide by the middle of April.  We
cannot extend support to people who are not giving talks.

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Estimated amount required for travel:
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Please return this form to:

Category Theory, 1991
Department of Math & Stat, McGill University
805 Sherbrooke St. W
Montreal, Quebec
Canada H3A 2K6

Email: mt16@mcgilla.bitnet    or    mt16@musica.mcgill.ca

Date: 10-SEP-1990 15:17:47.13
From: PJOHNSON@Wesleyan.bitnet

I would like to learn some fundamental facts (that don't seem to be
visible in Makkai and Pare', although I may be overlooking them)
about jus how sketchable is a generalization of equational:

1.  It seems clear that the models of an equational theory (a category
algebraic over Sets) is sketchable.  I'm thinking of a product sketch
on (the opposite of) the Kleisli category.  But is such a category
accessible, or only in the case the theory has rank  (a cardinal bound
on the arities of the operations) ?

2.  Are model categories for equational theories on an arbitrary base
category again sketchable over Sets via the same construction suggested
above?

3.  Is there such a thing as a canonical sketch, a kind of complete
syntactic description of a sketchable theory?  And if so, is there an
adunction between syntax and semantics?

Date:        Tue, 11 Sep 90 21:57:12 EDT
From:        Michael Barr <INHB@MUSICB.MCGILL.CA>

Dear Bob:

Since Paul Johnson put his question on the full net, let me answer it
there.

1. An equational theory is sketchable iff the theory has rank.
This follows from theorems of Pare and Makkai and is sort of obvious
anyway.

2. Yes, provided the base is accessible.

3. You had better ask Makkai or Pare.  But my guess is the following:
If you look at all the categories that are lambda-accessible, then there
will be canonical sketches built from the lambda-accessible models.  But
there are theories of arbitrarily high arities whose models are, for
example, the category of sets.  Sounds paradoxical?  Hint: the
underlying functor is not the usual, but is the functor represented by a
big (but still small) set.

Michael

Subject:     CT91
Date:        Tue, 18 Sep 90 11:17:46 EDT
From:        Tom Fox    <MT16@MUSICA.MCGILL.CA>

       CATEGORY THEORY 1991 - Clarification of dates

The conference will be held JUNE 23-30, 1991, as first announced.

Subject:     An answer, after 11 weeks absence
From: "Fred E.J. Linton" <FLINTON@Wesleyan.bitnet>
To: inhb@musicb.mcgill.ca

Mike,

On the very day I arrived in Iceland for the Jonsson symposium,
you asked me:

 This sounds like something you would have done.  If B is a category with
 a triple T and if K is the Kleisli category, then the category of
 T-algebras can be identified as the full subcategory of Func(K\op,Set)
 consisting of all functors R:K\op --> Set such that R o F\op: B\op -->
 Set is representable.  Can you give me a reference?  If I had SLN 80
 around, I would expect to find it there, but it is easier to ask you.

Now that I'm  back, I can answer: yep, that's what I did, more or less:
but not quite as you say -- that is, not literally the full subcategory
you say, but rather the pairs consisting of such functors as one entry
and a matching representing object as the other.  Done first in the
La Jolla volume, but just over  Sets , then in SLN 80 in the very first
article (An outline of functorial semantics, pp. 7-52), where I wrote  A
where you write  B , and finally, for the "relative category" setting, in
a preprint published by the Banach Center in Warsaw in 1974 entitled
Relative Functorial Semantics, III: Triples vs. Theories (three whole pages),
where I used  S  (suggesting  Sets ) as the notation for the closed, or
monoidal, or more generally just multilinear base category relatiove to
which all the relative category theory was to be done.  OK?

-- Fred
