Simplicial map

In the mathematical discipline of simplicial homology theory, a simplicial map is a map between simplicial complexes with the property that the images of the vertices of a simplex always span a simplex. Note that this implies that vertices have vertices for images.
Simplicial maps are thus determined by their effects on vertices. In particular, there are a finite number of simplicial maps between two given finite simplicial complexes.
Simplicial maps induce continuous maps between the underlying polyhedra of the simplicial complexes: one simply extends linearly using barycentric coordinates.
Simplicial maps which are bijective are called "simplicial isomorphisms".
Simplicial approximation.
Let formula_1 be a continuous map between the underlying polyhedra of simplicial complexes and let us write formula_2 for the star of a vertex. A simplicial map formula_3 such that formula_4, is called a simplicial approximation to formula_5.
A simplicial approximation is homotopic to the map it approximates.