Simplicial homotopy

In algebraic topology, a simplicial homotopy pg 23 is an analog of a homotopy between topological spaces for simplicial sets. If
 * $$f, g: X \to Y$$

are maps between simplicial sets, a simplicial homotopy from f to g is a map
 * $$h: X \times \Delta^{1} \to Y$$

such that the diagram (see ) 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.