An Overview of Higher Category Theory

In this short talk we will discuss the modern theory of infinity categories using quasicategories as first defined by Boardman and Vogt, and later developed extensively by Joyal and Lurie. We will discuss how infinity categories allow us to encode, at a very basic level, notions of homotopy coherence thereby uniting algebraic topology and category theory. The talk will culminate with a sketch of the proof of one of the fundamental results in the theory.