A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by two morphisms A⟶^α A' A' ⟶^(α') A'' without losing commutativity. Moreover, the short exact sequence 0⟶A⟶^α A' ⟶^(α') A'' ⟶0 is exact.

commutative diagram | exact sequence