Simplicial homotopy

In algebraic topology, a simplicial homotopypg 23 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 diagram (see ) formed by "f", "g" and "h" commute; the key is to use the diagram that results in formula_3 and formula_4 for all "x" in "X".