A proving technique in homological algebra which consists in looking for equivalent map compositions in commutative diagrams, and in exploiting the properties of injective, surjective and bijective homomorphisms and of exact sequences. The construction of the connecting homomorphism in the proof of the snake lemma is an example of diagram chasing.

commutative diagram | connecting homomorphism | diagram lemma | homological algebra | snake lemma | zig-zag lemma