Simplicial homotopy

In algebraic topology, a simplicial homotopy is an analog of a homotopy between topological spaces for simplicial sets. If

are maps between simplicial sets, a simplicial homotopy from f to g is a map

such that the obvious diagram (see [1]) formed by f, g and h commute; the key is to use the diagram that results in f ( x ) = h ( x , 0 ) and g ( x ) = h ( x , 1 ) for all x in X.