Introduction to Category Theory for Algebraic Topology (II)

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.

In this second talk, we will focus on adjunctions and associated universal constructions