freeResolution f
A homomorphism $f \colon M \to N$ of $R$-modules induces a morphism of chain complexes from any free resolution of $M$ to a free resolution of $N$. This method constructs this map of chain complexes.
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Taking free resolutions is a functor, up to homotopy, from the category of modules to the category of chain complexes. In the subsequent example, the composition of the induced chain maps $g$ and $g'$ happens to be equal to the induced map of the composition.
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Over a quotient ring, free resolutions are often infinite. Use the optional argument LengthLimit to obtain a truncation of the map between resolutions.
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The source of this document is in Complexes/ChainComplexMapDoc.m2:3504:0.