Take the 2-minute tour ×  Can all non-concrete categories be
constructed by taking a concrete category and identifying some
of its morphisms?   share|improve this question Or rather: Given
any category, can we find a suitable concrete category such that
... Personally, I doubt that. –  Hagen von Eitzen Dec 4 '12 at
10:06 All small categories are concrete. Categories that fail to
be locally small cannot possibly be quotients of concrete
categories, but it is possible to obtain non-locally-small
categories by localising concrete categories. –  Zhen Lin Dec 4
'12 at 10:33  1 Answer 1  The answer to this question is Yes you
can. The relevant paper is Ludek Kucera, Every category is a
factorization of a concrete one, Journal of Pure and Applied
Algebra, Volume 1, Issue 4, December 1971, Pages 373-376. You
may read the paper here:
http://www.sciencedirect.com/science/journal/00224049/1/4 .
However, this is a formal construction that does not seem to be
of much use in concrete problems (such as working in homotopy