Diagram Chasing

Diagram chasing is a method of mathematical proof used especially in homological algebra. Given a commutative diagram, a proof by diagram chasing involves formally using the properties of the diagram, such as injective or surjective maps, or exact sequences. One ends up "chasing" elements around the diagram, until the desired element is constructed. Examples of proofs by diagram chasing include the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.

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