Talk by Dr. Maria Yakerson
Date: 20.04.21 Time: 16.15 - 18.30 Room:
In different areas of mathematics it is convenient to work with categories, i.e., with sets of objects (possibly united by some property) and morphisms between them. However, when it comes to objects of topological nature, we often would like to consider the higher structure of morphisms between morphisms. For examples, higher structures are relevant when we work with topological spaces, continuous maps and homotopies, or with smooth manifolds, their cobordisms and diffeomorphisms between them. A generalization of a category that allows to encode the data of (infinitely many) higher morphisms is the notion of an infinity-category. In this talk, I will give a definition of an infinity-category and explain some of the main ideas behind this concept, as well as provide various examples.