Re: Terminology

[Jean Benabou <jean.benabou@wanadoo.fr>]

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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