Weakly exact categories and the snake lemma

TL;DR

This paper introduces weakly exact categories as a generalization of exact categories and proves the snake lemma within this new framework, enabling homological algebra applications.

Contribution

It defines weakly exact categories and establishes the snake lemma in this broader context, expanding the scope of homological algebra.

Findings

Snake lemma proven in weakly exact categories

Applications demonstrated for homological algebra

Generalization of exact categories introduced

Abstract

We generalize the notion of an exact category and introduce weakly exact categories. A proof of the snake lemma in this general setting is given. Some applications are given to illustrate how one can do homological algebra in a weakly exact category.