A LEISURELY INTRODUCTION TO SIMPLICIAL SETS

Simplicial sets are introduced in a way that should be pleasing to the formally-inclined. Care is taken to provide both the geometric intuition and the categorical details, laying a solid foundation for the reader to move on to more advanced topological or higher categorical applications. The highlight, and the only possibly non-standard content, is a unied presentation of every adjunction whose left adjoint has the category of simplicial sets as its domain: geometric realization and the total singular complex functor, the ordinary nerve and its left adjoint, the homotopy coherent nerve and its left adjoint, and subdivision and extension are some of the many examples that t within this framework.