Introduction
============

This chapter presents the category of finite simplicial complexes.

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

For detailed reading on simplicial complexes and their homology, we refer to
:cite:`hatcher02` and :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.