Simplicial map

In 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 finite maps, and there exists a finite amount of them which can be defined between any two given 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.

References

• Munkres, James R.: Elements of Algebraic Topology.