Dear Christopher, What I, personally, mean by structure is not the point. This word is used, very often, in mathematical texts. Sometimes giving the impression that it has a precise meaning on which the community of mathematicians agree. And I was sure there was at least one definition on which the majority of users did agree Then I received 3 answers all referring to: The joy of Cats, but different: For Carsten Führman, only faithfulness is required, which obviously is not enough Jiri Adamek adds: an isomorphism in S is an identity if its image is. I agree with this; but again not enough. Thomas Streicher adds a third condition, with which I would probably agree if was sure of the precise meaning of isofibration. Could you please, even at the risk of being pedantic say what you mean by that Many thanks to all
â€ژHi Jean - I don't quite understand this question but would like to. What do you mean by 'structure'? Thanks
Sent from my BlackBerry 10 smartphone on the O2 network. Original Message From: Jean Benabou Sent: Wednesday, 8 February 2017 16:18 To: Categories Reply To: Jean Benabou Subject: categories: Terminology
Dear all,
I'm sure the following question has been answered to. Could anyone give me a precise answer and references to this answer. Many thanks.
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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