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

Abstract

In this paper, we first construct some complete cotorson pairs on the category C N (G) of unbounded N -complexes of Grothendieck category G, from two given cotorsion pairs in G. Next as an application, we focus on particular homotopy categories and the existence of adjoint functors between them. These are an N -complex version of the results that were shown by Neeman in the category of ordinary complexes.

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

“…composition of any N consecutive maps gives the zero map. In recent years, many authors have focused on N -complexes as a generalization of some concepts in the Homology like derived category and homotopy category, see [22,17,3,5,25,24,34,33].…”