Snake lemma information

The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every...

stable categories, for example they are regular and they satisfy the snake lemma. The class of Abelian categories is closed under several categorical...

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...

stable categories; for example they are regular and they satisfy the snake lemma. The class of abelian categories is closed under several categorical...

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...

Abhyankar's lemma Fundamental lemma (Langlands program) Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Matrix determinant...

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...

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...

Clayburgh, portraying a mathematics professor, impeccably proves the snake lemma. Gross is a 1986 MacArthur Fellow. Gross, Zagier, and Dorian M. Goldfeld...

{\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...

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...

Chain complex Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Spectral sequence Abelian category...

category Abelian category Exact sequence Exact functor Snake lemma Nine lemma Five lemma Short five lemma Mitchell's embedding theorem Injective cogenerator...

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...

Differential module Five lemma Short five lemma Snake lemma Nine lemma Extension (algebra) Central extension Splitting lemma Projective module Injective...

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...

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 ∗...

condition should enter). The construction of β is by the usual argument (snake lemma). A similar construction applies to cohomology groups, this time increasing...

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...

formal categories, this theorization adopted the rule of satisfying the Snake lemma. Subsequently, this theorization strengthened the complementary concepts...

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...

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...

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...

become more of a mental state, preceding the actual utterance, akin to the lemma. Patañjali's writings also elaborate some principles of morphology (prakriyā)...

floret consists of the flower surrounded by two bracts, one external—the lemma—and one internal—the palea. The flowers are usually hermaphroditic—maize...

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...