Two chain complexes \( \mathbf{C} \) and \( \mathbf{D} \) are said to be isomorphic if there exists a chain isomorphism \( f: \mathbf{C} \to \mathbf{D} \). This means that \( f \) is a bijective linear map that commutes with the boundary maps, i.e., \( f_n: C_n
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