Algebra Seminar: Campbell -- A counterexample in quasi-category theory

Alexander Campbell (Macquarie University) 

Friday 31 May, 12-1pm, Place: Carslaw 375 

Title: A counterexample in quasi-category theory 

Abstract: In his pioneering work on the theory of quasi-categories (also known as
infinity-categories), Joyal left open the following question: is a morphism of
simplicial sets inner anodyne if and only if it is (i) a monomorphism, (ii) bijective on
0-simplices, and (iii) a weak categorical equivalence? In this talk, I will show that
the answer to this question is "no" by giving an example of a morphism of simplicial
sets which has the properties (i), (ii), and (iii), but which is not inner anodyne.
Furthermore, I will use this morphism to refute a plausible description of the
fibrations in Joyal’s model structure for quasi-categories.