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 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.

See also

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

External links

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