The Snake Lemma: A Categorical Approach
Abstract
The Snake Lemma is a fundamental result in homological algebra, traditionally proved by diagram chasing. In this work we present a detailed construction of the connecting morphism and prove the exactness of the resulting sequence using only universal properties. Most background material is standard and is included mainly to fix notation and prepare the categorical framework used in the proof. This note is primarily expository. Keywords: category theory, homological algebra, Snake Lemma, abelian categories, universal properties.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Rings
Modules
and Algebras
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 March 2026
- Language
- EN
- Document type
- Preprint