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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.

FiveLemmaShort.png

It follows immediately from the five lemma.

Referenced By

Five lemma | Four lemma | List of abstract algebra topics | List of algebraic topology topics | List of category theory topics | List of mathematical topics (S-U)

 

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Short five lemma".

 

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