Semi-Cartesian squares and the Snake Lemma

TL;DR

This paper introduces semi-cartesian squares within category theory to prove the snake lemma without relying on point-based or pseudo-element methods, offering a more abstract approach.

Contribution

It provides a novel proof of the snake lemma using semi-cartesian squares, avoiding traditional point-based or pseudo-element techniques.

Findings

Semi-cartesian squares are effectively used to prove the snake lemma.

The approach simplifies the proof by avoiding points and pseudo-elements.

The method aligns with categorical abstraction principles.

Abstract

The well-known snake lemma is proved entirely within category theory, without the help of "points with value in..." \`a la Grothendieck, nor pseudo-elements as in Guglielmetti & Zaganidis. Instead, we define and use consistently semi-cartesian squares, which were promoted by C. Chevalley.