Re: Sets vs. categories as a foundation

[EMAIL PROTECTED] (James Dolan) wrote:
> |I think I agree with George here.  One can take the set-theoretic
> |intuitions too far.  What about posets as categories?  The arrows
> |aren't imitations of functions, are they?
> sure they are; specifically, of inclusion functions between subsets
> (is one way to think of it).

A category can be thought of in many ways; for instance, that it's
nothing more than a typed monoid, or that it's an automaton whose
states are its objects and state transitions its arrows.

Trying to force the idea in one mould completely misses the point that
it's all these things, and therefore none of them at all.

Besides, everyone knows that categories are actually automata and
automata are categories.