Re: sketch theory

[Steve Lack <s.lack@uws.edu.au>]

Dear John,

You ask about a sketch for cartesian closed categories. Have a look at
at the paper "A presentation of topoi as algebraic relative to categories or
graphs (Dubuc-Kelly, J. Alg. 81: 420-433, 1983). This describes something
even tighter: the category of cartesian closed categories is monadic over
the category of graphs.

If you look at the description given in that paper, it clearly contains a
sketch for cartesian closed categories (this depends heavily paper on the
paper Algebres Graphique of Albert Burroni). In fact the Dubuc-Kelly paper
also describes a notion of presentation for finitary monads on Cat; this was
later developed by Kelly and Power into a fully-fledged theory of
presentations for finitary enriched monads on locally finitely preseentable
categories, in their paper " Adjunctions whose counits are coequalizers, and
presentations of finitary enriched monads" (JPAA 89:163-179, 1993).

Regards,

Steve Lack.


On 22/05/09 5:43 AM, "John Baez" <john.c.baez@gmail.com> wrote:

> Dear Categorists -
>
> Andrei Rodin pointed out this paper by Charles Wells:
>
> http://www.cwru.edu/artsci/math/wells/pub/pdf/sketch.pdf
>
> I took a look.  In section 4.1 it mentions that people have given a finite
> limits sketch for cartesian closed categories.  I'm curious about how this
> works,  Unfortunately the list of references given here is quite long.  Can
> anyone help me find a reference on a sketch for CCC's?
>
> Best,
> jb
>
>