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 ${\displaystyle f(x)=h(x,0)}$ and ${\displaystyle g(x)=h(x,1)}$ for all x in X.

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