9 Feb
2017
9 Feb
'17
3:34 a.m.
Dear Jean, The simplest answer is: faithful. But a better one (in view of `everything up to isomorphism') is: faithful and amnestic. The latter means that p reflects identity morphisms: an isomorphism in S is an identity if its image by p is. See The Joy of Cats (free on the web). Best, Jiri
QUESTION Let p: S --> X be a functor. What conditions should satisfy p to be called a structure functor, i.e. such that every object s of S can be thought of as a structure on the object p(s).
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