Introduction to Category Theory for Algebraic Topology (I)

Cameron Calk (LIS)

Summary

In this introduction to category theory, we will first cover the basic definitions : categories, functors and natural transformations. Then we will move on to adjunctions and (co-)limits, which, due to the notion of universal property, are central to the expressive power of category theory. Finally, we will discuss the Yoneda lemma, a simple (yet mysterious) fundamental observation about categories, and presheaves, special functors which, intuitively, describe glueing operations such as those encountered in the construction of simplicial or cubical complexes.

The goal of this talk is to familiarise the audience with the basic notions and vocabulary of category theory while providing concrete examples, which will (almost exclusively) be of topological or order-theoretic nature. At the end of the session, we will determine the subject of the follow-up talk depending on the interests of the TopoCS community.