Encyclopedia > Short five lemma

Article Content

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), 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.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Etude

... 18th century, most notably by Carl Czerny, but it was Frederic Chopin who transformed the etude into a virtuoso showpiece for his chosen instrument, the piano. Chopin wrote ...