FOM: small category theory
Kanovei
kanovei at wmfiz4.math.uni-wuppertal.de
Wed May 5 03:29:41 EDT 1999
Date: Wed, 05 May 1999 00:04:05 -0700
From: Till Mossakowski <till at informatik.uni-bremen.de>
> Several ideas for
> the foundation of category theory have been proposed: (...)
1) As for vNBG, why not to consider a type theoretic
class extension of ZFC, ie, level 0 = sets, level 1=
classes of sets, level 2 = classes of level 1 elements,
etc, but, to stick to ZFC, still only set quantifiers
are allowed in Comprehension for all levels.
Furthermore, one can then try to abolish the levels
and consider this as a kind of Z extension of the ZFC
set universe, still with only set quantifiers working.
2) How about the following Borel-motivated approach ?
Consider only those categories whose objects and
morphisms between them are Borel structures in
separable metric spaces.
After all, the major body of mathematics can be
coded by Borel sets, if not by natural numbers.
Is there an immediate drawback ?
This is clearly not for those who develops the
category theory for its own sake, but could it
work for number-theoretic applications ?
V.Kanovei
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