The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every...
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Homological algebra (section Snake lemma)
stable categories, for example they are regular and they satisfy the snake lemma. The class of Abelian categories is closed under several categorical...
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lemma can then be used to determine the unknown homology groups. Short five lemma, a special case of the five lemma for short exact sequences Snake lemma...
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version of Zassenhaus' butterfly lemma. In this form, Goursat's lemma also implies the snake lemma. Goursat's lemma for groups can be stated as follows...
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Abhyankar's lemma Fundamental lemma (Langlands program) Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Yoneda lemma Matrix...
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interchanged in the above 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...
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a student who raised objections during Jill Clayburgh's proof of the snake lemma in the film It's My Turn. He was the novice observer Richard Lymangood...
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stable categories; for example they are regular and they satisfy the snake lemma. The class of abelian categories is closed under several categorical...
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short exact sequences into long exact sequences is a consequence of the snake lemma. This tells us that the collection of derived functors is a δ-functor...
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include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma. In higher category theory, one considers not...
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the lemma arises from the "zig-zag" behavior of the maps in the sequence. A variant version of the zig-zag lemma is commonly known as the "snake lemma" (it...
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abelian categories, such as the nine lemma, the five lemma, and their consequences hold true in Grp. The snake lemma however is not true in Grp.[dubious...
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Clayburgh, portraying a mathematics professor, impeccably proves the snake lemma. Gross is a 1986 MacArthur Fellow. Gross, Zagier, and Dorian M. Goldfeld...
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Differential module Five lemma Short five lemma Snake lemma Nine lemma Extension (algebra) Central extension Splitting lemma Projective module Injective...
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romantic comedy, It's My Turn, in which she teaches the proof of the snake lemma. Novelist Eleanor Bergstein, who had written the screenplay, was delighted...
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Chain complex Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Spectral sequence Abelian category...
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category Abelian category Exact sequence Exact functor Snake lemma Nine lemma Five lemma Short five lemma Mitchell's embedding theorem Injective cogenerator...
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{\displaystyle A} . Then the snake lemma is invoked to show that the simultaneous resolution constructed so far has exact rows. Nine lemma Cartan, Henri; Eilenberg...
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condition should enter). The construction of β is by the usual argument (snake lemma). A similar construction applies to cohomology groups, this time increasing...
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sequence splits. The snake lemma shows how a commutative diagram with two exact rows gives rise to a longer exact sequence. The nine lemma is a special case...
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rise to a chain complex of short exact sequences. An application of the snake lemma then yields a long exact sequence ⋯ → H n ( A ) → i ∗ H n ( X ) → j ∗...
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q : Hq(C•) → Hq+1(A•). These are the connecting homomorphisms from the snake lemma, and together with the maps A• → B• → C•, they give a sequence: ⋯ → H...
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division ring. Shapiro Shapiro's lemma sheaf of modules sheaf of modules snake snake lemma socle The socle is the largest semisimple submodule. semisimple A...
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formal categories, this theorization adopted the rule of satisfying the Snake lemma. Subsequently, this theorization strengthened the complementary concepts...
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Geb (category Snake gods)
member of the Ennead of Heliopolis. He could also be considered a father of snakes. It was believed in ancient Egypt that Geb's laughter created earthquakes...
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Cantor's diagonal argument (redirect from Cantor's snake)
digit is zero or one). He begins with a constructive proof of the following lemma: If s1, s2, ... , sn, ... is any enumeration of elements from T, then an...
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managers in the United States Hensel's lemma, a result in modular arithmetic Hensel's snake (Ditaxodon taeniatus), a snake endemic to southern Brazil Henselian...
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term. Moreover it remains to be determined what the original shape of the lemma was in early Slavic, which obfuscates its history and linguistic relationships...
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floret consists of the flower surrounded by two bracts, one external—the lemma—and one internal—the palea. The flowers are usually hermaphroditic—maize...
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genus). Adjectives vary according to gender, and in most cases only the lemma form (nominative singular masculine form) is listed here. 1st-and-2nd-declension...
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