A counterexample in quasi-category theory

Alexander Campbell – 15 May 2019

In this talk I will 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, I will use this morphism to answer a few related open questions, e.g. I will refute a plausible description of the class of fibrations in Joyal's model structure for quasi-categories.