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Nov 16, 2023 at 19:19 comment added Peter LeFanu Lumsdaine Another possibility is to take forgetful functors to be just the first-projection functors from the total category of a displayed category to its base. Actual usage in practice seems to vary somewhere between “precisely just these functors” and “anything isomorphic (sic!) to such a functor”. This is deliberately not invariant under equivalence, since the usage of “forgetful” in practice is not so.
Nov 16, 2023 at 18:08 history edited Tobias Fritz CC BY-SA 4.0
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S Mar 10, 2023 at 7:34 history answered Tobias Fritz CC BY-SA 4.0
S Mar 10, 2023 at 7:34 history made wiki Post Made Community Wiki by Tobias Fritz