Simplicial homotopy

In algebraic topology, a simplicial homotopy 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

$h: X \times \triangle^{1} \to Y$

such that the obvious 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.

See also

• Dold–Kan correspondence (under which a chain homotopy corresponds to a simplicial homotopy)

External links

• http://ncatlab.org/nlab/show/simplicial+homotopy