Short five lemma

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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. Image:FiveLemmaShort.png It follows immediately from the five lemma.