Suppose α:C_*->D_* and β:C_*->D_* are two chain homomorphisms. Then a chain homotopy is given by a sequence of maps δ_p :C_p->D_(p - 1) such that d_D °δ + δ°d_C = α - β, where d denotes the boundary operator.

chain complex | chain equivalence | chain homomorphism | homotopy | snake lemma