On Cotorsion Pairs of Chain Complexes

Abstract

Abstract. In the paper we first construct a new cotorsion pair, in the category of chain complexes, from two given cotorsion pairs in the category of modules, and then we consider completeness of such pairs under certain conditions.

⊗-Pure model structure on the category of N -complexes

“…Gillespie's work further extended this concept to exact categories. Numerous examples of cotorsion pairs and their corresponding model structures on the category of complexes were introduced based on Hovey's theorem and Gillespie's work., see [16,29,12,13,14,9,4,32]. One of the model structures constructed in the category of complexes of a closed symmetric monoidal Grothendieck category was introduced by Estrada, Gillespie, and Odabasi in [11].…”

Cotorsion pairs and adjoint functors in the homotopy category of N-complexes

“…In 2002, Hovey established a correspondence between the theories of cotorsion pairs and model structures (Hovey's theorem [Hov02]). So the study of cotorsion pairs on the category of complexes is important, see [Gil04], [Gil06], [Gil08], [EER1], [EEI], [EAPT], [St], [YD15]. Since the concept of N -complexes is a generalization of the ordinary complexes, it is natural to study cotorsion pairs on the category of N -complexes.…”