Chase's lemma and its context

TL;DR

This paper clarifies the context and technical details of Chase's lemma, a key tool in abelian categories for relating (co)product properties to chain conditions, often overlooked in literature.

Contribution

It explicitly discusses the often-neglected technical context of Chase's lemma in abelian categories.

Findings

Clarifies the technical context of Chase's lemma.

Highlights the importance of the lemma in relating (co)products to chain conditions.

Provides insights into the lemma's applications in category theory.

Abstract

Chase's lemma provides a powerful tool for translating properties of (co)products in abelian categories into chain conditions. This note discusses the context in which the lemma is used, making explicit what is often neglected in the literature because of its technical nature.