Brown representability for triangulated categories with a linear action by a graded ring

TL;DR

This paper establishes criteria for when a functor can be represented in a strongly generated triangulated category with a graded ring action, including applications and examples.

Contribution

It provides necessary and sufficient conditions for functor representability in such categories, advancing understanding of their structure and applications.

Findings

Criteria for functor representability established

Applications demonstrate practical relevance

Examples illustrate theoretical results

Abstract

In this paper we give necessary and sufficient conditions for a functor to be representable in a strongly generated triangulated category which has a linear action by a graded ring, and we discuss some applications and examples.