Ivan Kobe: Grothendieck-Maltsiniotis (ω,n)-categories

Abstract: Grothendieck-Maltsiniotis (ω,n)-categories are an algebraic model of higher categories. They are of particular interest because they can be recovered as models of a certain type theory, which can be used for the development of synthetic category theory.

In this talk, I will define these structures and explain some of their key properties. I will also discuss their close relationship with topologically enriched categories, whose homotopy theory is well-studied. The correspondence between the two models arises via a realization ⊣ nerve construction which in particular provides a wealth of examples.