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- Nine_lemma abstract "In mathematics, the nine lemma is a statement about commutative diagrams and exact sequences valid in any abelian category, as well as in the category of groups. It states: ifFile:Nine lemma.pngis a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well. Likewise, if all columns as well as the two top rows are exact, then the bottom row is exact as well.The nine lemma can be proved by direct diagram chasing, or by applying the snake lemma (to the two bottom rows in the first case, and to the two top rows in the second case).Linderholm (p. 201) offers a satirical view of the nine lemma:"Draw a noughts-and-crosses board... Do not fill it in with noughts and crosses... Instead, use curved arrows... Wave your hands about in complicated patterns over this board. Make some noughts, but not in the squares; put them at both ends of the horizontal and vertical lines. Make faces. You have now proved:(a) the Nine Lemma(b) the Sixteen Lemma(c) the Twenty-five Lemma..."".
- Nine_lemma thumbnail Nine_lemma.png?width=300.
- Nine_lemma wikiPageID "454673".
- Nine_lemma wikiPageRevisionID "543517028".
- Nine_lemma hasPhotoCollection Nine_lemma.
- Nine_lemma subject Category:Homological_algebra.
- Nine_lemma subject Category:Lemmas.
- Nine_lemma type Abstraction100002137.
- Nine_lemma type Communication100033020.
- Nine_lemma type Lemma106751833.
- Nine_lemma type Lemmas.
- Nine_lemma type Message106598915.
- Nine_lemma type Proposition106750804.
- Nine_lemma type Statement106722453.
- Nine_lemma comment "In mathematics, the nine lemma is a statement about commutative diagrams and exact sequences valid in any abelian category, as well as in the category of groups. It states: ifFile:Nine lemma.pngis a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well.".
- Nine_lemma label "Neunerlemma".
- Nine_lemma label "Nine lemma".
- Nine_lemma label "九引理".
- Nine_lemma sameAs Neunerlemma.
- Nine_lemma sameAs m.02bht_.
- Nine_lemma sameAs Q2645980.
- Nine_lemma sameAs Q2645980.
- Nine_lemma sameAs Nine_lemma.
- Nine_lemma wasDerivedFrom Nine_lemma?oldid=543517028.
- Nine_lemma depiction Nine_lemma.png.
- Nine_lemma isPrimaryTopicOf Nine_lemma.
