title: Simplicial homotopy
text: # Simplicial homotopy
  
  In algebraic topology, a simplicial $homotopy^{pg23}$ 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.
  
  