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.
Rafael Nunes Alecrim Monteiro (Wed,) studied this question.