Jeroen Hekking: A first encounter of ∞-categories

Abstract: An ∞-category should be something like a collection of objects, together with 0-morphisms between those objects, then 1-morphisms between those 0-morphisms, etc. It is used in homotopy theory as a convenient and natural language to deal with notions of equivalences that are weaker than identity or isomorphisms.  In this talk I will give a gentle introduction to two approaches to ∞-categories: quasi-cateogories and simplicially enriched categories, and will say something about how these two are related. I will begin with a reminder on the necessary categorical and simplicial background for this.