Let "S" and "T" be simplicial complexes. A simplicial map "f" from "S" to "T" is a function from the vertex set of "S" to the vertex set of "T" such that the image of each simplex in "S" (viewed as a set of vertices) is a simplex in "T". A simplicial map "f": "S" → "T" determines a homomorphism of homology groups "H""k"("S") → "H""k"("T") for each integer "k". This is the homomorphism associated to a chain map from the chain complex of "S" to the chain complex of "T". Explicitly, this chain map is given on "k"-chains by