September 10, 2025

Homotopy pure complexes and derived categories

Key Points

Homotopy pure projective and injective complexes are crucial for understanding derived categories.
The pure derived category is equivalent to the category of homotopy pure projective complexes.
Equivalent characterizations highlight the structural properties of homotopy pure complexes.
Finding relationships among these categories may lead to insights in homotopy theory.

Abstract

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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Cite This Study

Lu et al. (Tue,) studied this question.

synapsesocial.com/papers/68c184069b7b07f3a06104b4 https://doi.org/https://doi.org/10.1080/00927872.2025.2547698

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