FOM: Re: Picturing categorical set theory, reply to Silver

[Colin McLarty]

Charles Silver wrote:

        Responding to my sketch of motives for categorical set theory,
when I asked if it made sense

>	I think so.  But, I'm looking for something slightly different. 
>Perhaps what I'm looking for isn't there.  The kind of thing I'm looking
>for is an underlying *conception* of function that is *explicated* by
>category theory.

        Well, don't confuse general category theory (or even categorical
foundations) with the much more specific topic of categorical set theory.
You'll end up calling me a squid throwing ink in your eyes. (Actually, I
adore squid, so if you are what you eat I may be guilty...) Certainly no
specific picture motivates general category theory, where the whole idea is
to have a huge range of applications. I'll give a further motivation for the
functions of categorical set theory, since your original question asked for
comparison with set theory books.

        A function from a set M onto a set S is a kind of rule by which each
element of M is bound to a unique element of N. And an "element" is
understood to be any distinct object of thought, none of its properties are
relevant but that it is distinct from every other object. Thus these
functions are unconstrained by any kind of continuity or algebraic structure
preservation.


        To get much more specific would mean to give actual axioms, as I
have done in various articles and my book.

Colin