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] and [Armstrong, 1983].

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.