Dear Jean, unless there is a technical meaning of "structure" I'm not aware of, the answer may be "Concrete categories" in the sense of Adámek, Herrlich, and Strecker: http://katmat.math.uni-bremen.de/acc/acc.pdf. A concrete category is just a faithful functor, but a remarkable amount of theory can be build on that notion. In particular, a classification of "algebra-like" and "space-like" structures is already possible at that level. On Wed, Feb 8, 2017 at 4:56 PM Jean Benabou <jean.benabou@wanadoo.fr> wrote:
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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