Description
In the example below, we have a map between two modules and extend it to a map between projective resolutions of the two modules. Then
source gives the source of the map of chain complexes.
i1 : R = ZZ[x,y,z];

i2 : M = R^1/(x,y,z);

i3 : N = R^1/(x^2,y^2,x*y*z,z^2);

i4 : g = map(N,M,x*y);
o4 : Matrix N < M

i5 : f = res g;

i6 : source f
1 3 3 1
o6 = R < R < R < R < 0
0 1 2 3 4
o6 : ChainComplex

(That was an expensive way of resolving
M.)