Prove Lemma 44.14 Let A' be a subcomplex of a chain complex A. Let j be the

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Prove Lemma 44.14 

Let A' be a subcomplex of a chain complex A. Let j be the collection of natural homomorphisms jk : Ak → (Ak/A'K). Then 

jk = 1k ∂̅kjthat is, j commutes with ∂. 

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