Cotorsion Classes in Higher Homological Algebra

TL;DR

This paper introduces and explores the concept of cotorsion classes within higher homological algebra, establishing foundational properties and extending classical lemmas to the higher-dimensional setting.

Contribution

It defines n-cotorsion classes in higher homological algebra and proves a higher version of Wakamatsu's Lemma, connecting to wide subcategories.

Findings

n-cotorsion classes satisfy expected properties

A higher Wakamatsu's Lemma is established

Connections with wide subcategories are analyzed

Abstract

In this note, the notion of cotorsion classes is introduced into the higher homological algebra. Our results motivate the definition, showing that this notion of $n$-cotorsion classes satisfies usual properties one could expect. In particular, a higher version of Wakamatsu's Lemma is proved. Connections with wide subcategories are also studied.