Five Lemma

A diagram-chasing result in homological algebra: given a commutative diagram of two exact rows A1→A2→A3→A4→A5 and B1→B2→B3→B4→B5 with vertical maps f_i: A_i→B_i, if f1, f2, f4, f5 are isomorphisms and the middle maps satisfy the appropriate surjectivity/injectivity hypotheses, then f3 is an isomorphism.

A diagram-chasing lemma stating that in a commutative diagram of two exact rows with five objects each, if four of the five vertical maps are isomorphisms (or under the standard mono/epi hypotheses) then the remaining middle vertical map is also an isomorphism.