Simplicial homotopy
In algebraic topology, a simplicial homotopy is an analog of a homotopy between topological spaces for simplicial sets. Precisely,pg 23 if f , g : X → Y {\displaystyle f,g:X\to Y} are maps between simplicial sets, a simplicial homotopy from f to g is a map h : X × Δ 1 → Y {\displaystyle h:X\times \Delta ^{1}\to Y} such that the restriction of h {\displaystyle h} along X ≃ X × Δ 0 ↪ 0 X × Δ 1 {\displaystyle X\simeq X\times \Delta ^{0}{\overset {0}{\hookrightarrow }}X\times \Delta ^{1}} is f {\displaystyle f} and the restriction along 1 {\displaystyle 1} is g {\displaystyle g} ; see [1].