categories: Re: Characterizing FinSet up to equivalence

[Toby Bartels <toby@math.ucr.edu>]

Vaughan Pratt wrote in part:

>However I disagree that the assumption of finiteness constitutes smuggling
>in FinSet.  A tiny part of it, fine, but that's a long way from smuggling in
>the whole notion of function.

Indeed, so long as category theory begins with <Let Ob(C) be a set.>,
then some set theory can't help but be smuggled in.
If you say <FinSet is the free finitely complete category on 1 object.>,
then you're asking Mor(D) to be a finite set
(where D is the diagram in a limit being considered),
but you already have to ask Mor(D) to be a set,
so this doesn't smuggle in any more set theory than was already there.


-- Toby Bartels
   toby@math.ucr.edu