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...

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

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...

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...

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...

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

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...

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...

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...

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

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...

{\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...

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

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 ∗...

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...

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...

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

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...

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...

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...

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...