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