[FOM] CAT co-well-powered?

mhebert mhebert at aucegypt.edu
Sat Sep 13 04:14:46 EDT 2003

>On Thu, 11 Sep 2003, HAUCOURT emmanuel wrote:
>> Is CAT (the category of small categories) co-well-powered?
>> Is anyone has references about epic of CAT?

In addition to the papers suggested by Todd Wilson, here is a recent paper 
specifically about epis in CAT:
Bernarczyk, M. et al., Generalized congruences - epimorphisms in CAT, Theory 
and Appl. of Categories 5 (1999), No 11, 266-280.

About Todd's answer:
>[...] Since epimorphisms are characterized by having dominions equal to
>their ranges, this gives a description of epis in CAT, and shows, in
>particular, that their codomains are bounded [...]

just in case: he probably meant "[...] dominions equal to their *codomains*, 
this gives [...]".

Michel Hebert

More information about the FOM mailing list