Partial answer to Jean Benabou

[Andree Ehresmann <andree.ehresmann@u-picardie.fr>]

In answer to the question raised by Jean:

>if C is a category, what does  one need to assume on a subcategory
V of C to be able to construct an analogous C/V and what structure does
it inherit ?

Charles Ehresmann had studied the problem of the existence of a quotient =
(or at
least 'quasi-quotient') category of a category by a sub-category, which h=
ad led
to the introduction of the notion of a "proper subcategory" (generalizing
distinguished sub-groups). His results, 	summarized in a Note (CRAS Paris=
 260,
2116) are developed in the paper on non-abelian cohomology "Cohomologie a
valeurs dans une categorie dominee" (Collloque Topologie Bruxelles, CBRM =
1866)
. Both papers are reprinted in "Charles Ehresmann: Oeuvres completes et
commentees" Part III-2 (and partially taken back in his book "Categories =
et
structures", Dunod 1965).
With all my best wishes
Andree Ehresmann.