26 Nov
2001
26 Nov
'01
12:39 p.m.
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