Let \(K\) and \(L\) be simplicial complexes with vertex sets \(V(K)\) and \(V(L)\). A simplicial map \(f\colon K\to L\) is a map \(f\colon V(K)\to V(L)\) such that whenever \(v_0,\ldots,v_k\) are the vertices of a simplex of \(K\), the points \(f(v_0),\ldots,f(v_k)\), not necessarily distinct, are the vertices of a simplex of \(L\).
A simplicial map extends to a continuous map \(\abs{K}\to\abs{L}\) of underlying spaces that is affine on each simplex: \(\sum_it_iv_i\mapsto\sum_it_if(v_i)\) for \(t_i\geq0\) with \(\sum_it_i=1\) [@Mun84].