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This research identifies equivalent characterizations of homotopy pure complexes, showing implications for derived categories.
We introduce and study the notions of homotopy pure projective complexes and homotopy pure injective complexes. We give some equivalent characterizations of the above complexes. As an application, we show that the pure derived category can be realized as the category of homotopy pure projective complexes or homotopy pure injective complexes.
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Lu et al. (2025) studied this question.
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