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Given two chain complexes A {\displaystyle A} and B {\displaystyle B} , a homomorphism of chain complexes h : A → B {\displaystyle h:A\to B} associates, for every n {\displaystyle n} , a homomorphism h n : A n → B n {\displaystyle h_{n}:A_{n}\to B_{n}} such that the h n {\displaystyle h_{n}} commutes with the d {\displaystyle d} maps.
