Short five lemma

In mathematics, especially homological algebra and other applications of Abelian category theory, the short five lemma is a special case of the five lemma. It states that for the following commutative diagram (in any Abelian category, or in the category of groups), if the rows are exact, and if g and h are isomorphisms, then f is an isomorphism as well.

It follows immediately from the five lemma.