Simplicial Map

(Simplicial Homology)

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Simplicial Homology
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What is 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.

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algebraic topologysimplicial homology

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