 Then "f" is homotopic to a cellular map "(X,A)"→"(Y,B)".To see this, restrict "f" to "A" and use cellular approximation to obtain a homotopy of "f" to a cellular map on "A".Use the homotopy extension property to extend this homotopy to all of "X", and apply cellular approximation again to obtain a map cellular on "X", but without violating the cellular property on "A".