# Introduction

This chapter presents the category of finite simplicial complexes.

We define an abstract simplicial complex $K$ to be a subset of the power set of some set $V$ of vertices, with the property that if $S\in K$ and $T\subset S$ then $T\in K$.

For detailed reading on simplicial complexes and their homology, we refer to [[Hatcher, 2002](../../references.md#cite-hatcher02)] and [[Armstrong, 1983](../../references.md#cite-armstrong83)].

Simplicial complexes may be defined over any `SetEnum`, however, many of the construction methods operate over `SetEnum[RngIntElt]`. The handbook refers to such simplicial complexes as *normalized*.

A simplicial complex carries the category name `SmpCpx`. Constructors and package internal functions guarantee that the closure under subsets relation is kept intact.