Dear Jean, in Remark 13.18 of their book on "Algebraic Theories" Adamek, Rosicky and Vitale suggest the following conditions 1) p faithful (what they call "concrete over X") 2) p-vertical isos are identities (what they call "amnestic")) 3) p is an isofibration (what they call "transportable") These seem to be reasonable conditions validated by most examples. Does this confirm with your intuition? Thomas
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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