A counterexample in quasi-category theory

Campbell, Alexander

doi:10.1090/proc/14692

A counterexample in quasi-category theory
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Proc. Amer. Math. Soc. 148 (2020), 37-40 Request permission

Abstract:

We give an example of a morphism of simplicial sets which is a monomorphism, bijective on $0$-simplices, and a weak categorical equivalence, but which is not inner anodyne. This answers an open question of Joyal. Furthermore, we use this morphism to refute a plausible description of the class of fibrations in Joyal’s model structure for quasi-categories.

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