Julian Komaromy: A Gentle Introduction to Infinity-Categories

Abstract:

Infinity-categories have become popular in many areas of mathematics such as algebraic topology, algebraic geometry and type theory for their ability to capture "higher order" information. The classical example is spaces, continuous maps, homotopies (continuous deformations) between them, homotopies between homotopies, and so on... The resulting theory provides a rich setting for working up to some sort of equivalence, e.g. homotopy equivalence. In this gentle introduction, we will talk mostly about why and where infinity-categories are useful instead of caring too much about rigorous definitions.
Note: the talk should be accessible to everyone. Ideally, one would have seen some basic topology and the definition of a category.