Every map of CW complexes is homotopic to a cellular map, relative to any already-cellular subcomplex.Suggest a slogan
Every map \(f\colon X\to Y\) of CW complexes is homotopic to a cellular map. If \(f\) is already cellular on a subcomplex \(A\subseteq X\), the homotopy may be taken to be stationary on \(A\) [@Hat02].