For questions about proofs using equivalent map compositions in commutative diagrams in homological algebra, or in category theory in general.
Diagram chasing is a method for proving statements using equivalent map compositions in commutative diagrams, thereby using properties of the diagram such as injective or surjective maps, or exact sequences. Mostly used in homological algebra and category theory. Examples include the five lemma, the snake lemma and the nine lemma.
See also Diagram Chasing at MathWorld.