Lemma 6.2.8. The homotopy category of \(\Kk (\Aa )\) is the category whose objects are chain complexes and whose morphisms are chain maps modulo chain homotopy.
Proof. As in the proof of Corollary 2.3.7, this follows from the observation that a functor \(\Ch (\Aa ) \to C\) into a 1-category \(C\) inverts chain homotopy equivalences if and only if it identifies chain homotopic chain maps. □
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