5 Oct
2016
5 Oct
'16
8:45 p.m.
Michael Barr hat am 04.10.16 um 14:21 Uhr geschrieben:
We all know that if Hom(A,-) is naturally equivalent to Hom(B,-), then A is isomorphic to B. But can you find a category in which for each object C, Hom(A,C) is isomorphic to Hom(B,C) but no naturality of the isomorphism without A being isomorphic to B?
Yes, you can. Take a category with your two objects A and B, Hom(X,Y) the set of natural numbers, composition being addition. Now remove 0 from Hom(A,B). Best regards Thorsten [For admin and other information see: http://www.mta.ca/~cat-dist/ ]