A diagram lemma which states that, given the above commutative diagram with exact rows, the following holds: 1. If α is surjective, and β and δ are injective, then γ is injective; 2. If δ is injective, and α and γ are surjective, then β is surjective. This lemma is closely related to the five lemma, which is based on a similar diagram obtained by adding a single column.

commutative diagram | diagram lemma | exact sequence | five lemma