URegina Topology & Geometry Seminar: Francis Bischoff

A common theme in homotopy theory is to record not just whether two objects are equivalent, but also *how* they are equivalent. For instance, we can consider maps between spaces, homotopies between maps, homotopies between homotopies, and so on. An infinity-category is a way of encoding such data into mapping spaces between objects.

Quillen introduced model categories as a framework for doing homotopy theory. While we can do a lot with model categories, it is sometimes convenient to work directly at the level of infinity-categories. In this talk, I will motivate infinity-categories using examples. I will then provide an introduction to simplicial sets, which will serve as foundation for the rest of the lecture series.