General Topology/Simplicial complexes

There are several types of simplicial complexes. semisimplicial set A semisimplicial set is a contravariant functor from the category of finite sets and monotone maps to . Δ-complex A Δ-complex is a topological space together with a family of functions such that for each , the set is the standard simplex of a certain dimension with the subspace topology induced by the topology of on it, for each there exists a unique and (the interior) so that , the topology of coincides with the final topology with respect to the , and if is not the trivial simplex and is its dimension, then the map arising from mapping to any face of and then applying equals for some .