Dear Jean and Jiri, As we know there is no such notion accepted by everybody. I would probably vote for faithful + amnestic + iso-fibration. Best regards, George -------------------------------------------------- From: "Jir? Ad?mek" <j.adamek@tu-bs.de> Sent: Wednesday, February 8, 2017 6:34 PM To: "categories net" <categories@mta.ca> Subject: categories: Re: Terminology
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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