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Sep 11, 2015 at 10:39 comment added Edoardo Lanari They are assumed to be fibrations, I skipped this detail since it seemed unessential to the proof. The reference is "Fibrations and Yoneda's lemma in an ∞-cosmos" by Riehl and Verity, Lemma 4.2.6.
Sep 11, 2015 at 10:34 comment added Zhen Lin It's not true. If it were true then every morphism of groupoids would be a fibration.
Sep 11, 2015 at 9:39 history asked Edoardo Lanari CC BY-SA 3.0