Re: sketch theory

[John Baez <john.c.baez@gmail.com>]

Steve Lack writes:

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.
>

Thanks!

And thanks to everyone else for their helpful comments.  I'm behind on
answering my emails.

In this approach, does each pair of objects in a ccc come with a chosen
product and exponential? Are the morphisms of ccc's are required to preserve
these on the nose?

At first I was a bit shocked to hear of a sketch for ccc's, because the
internal hom is contravariant in one variable.  But I guess that as long as
we treat ccc's purely 1-categorically that's no problem.  But then I guess
we pay the price of "undue strictness".  Right?

Best,
jb