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Oct 26, 2018 at 17:29 vote accept Arrow
Oct 26, 2018 at 13:45 answer added Simon Henry timeline score: 8
Oct 26, 2018 at 10:24 comment added Arrow @ArnaudD. I am happy to add such assumptions, but since I don't know the theory of fibrations well, I am hoping for an answer which will explain them and their consequences.
Oct 26, 2018 at 9:44 comment added Arnaud D. Just a thought: in the case of the codomain fibration, what makes a difference is often not only the properties you mention but also whether they are stable under pullbacks. So for a general fibration maybe you'd have to ask that the fibration reflects the property of $f$, at least for cartesian arrows.
Oct 26, 2018 at 8:36 history asked Arrow CC BY-SA 4.0