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

## TL;DR

This paper constructs complete cotorsion pairs in the homotopy category of unbounded N-complexes over a Grothendieck category and explores the existence of adjoint functors, extending classical results to N-complexes.

## Contribution

It introduces a method to derive cotorsion pairs in N-complex categories from those in the base category and studies adjoint functors in this context.

## Key findings

- Constructed complete cotorsion pairs in N-complex categories.
- Established the existence of adjoint functors between homotopy categories of N-complexes.
- Extended classical results on adjoint functors to the setting of N-complexes.

## Abstract

In this paper, we first construct some complete cotorson pairs on the category $\mathbb{C}_N(\mathcal{G})$ of unbounded $N$-complexes of Grothendieck category $\mathcal{G}$, from two given cotorsion pairs in $\mathcal{G}$. 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 were shown by Neeman in the category of ordinary complexes.