Simplicial Sets

Abstract

Simplicial sets form a very convenient tool to study the homotopy theory of topological spaces. In this chapter we will present an introduction to the theory of simplicial sets. We assume some basic acquaintance with the language of category theory, but no prior knowledge of simplicial sets on the side of the reader. We present the basic definitions and constructions, including the geometric realization of a simplicial set, the nerve of a category, and the description of the product of two simplicial sets in terms of shuffles.