abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams. The five lemma is not only valid for abelian...

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...

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

of vector spaces over a given field) or in the category of groups. The five lemma states that, if the rows are exact, m and p are isomorphisms, l is an...

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

Lemma (b) the Sixteen Lemma (c) the Twenty-five Lemma... There are two variants of nine lemma: sharp nine lemma and symmetric nine lemma (see Lemmas 3...

chasing 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...

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

formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all...

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

Euler's formula Euler's four-square identity Euler's theorem Five color theorem Five lemma Fundamental theorem of arithmetic Gauss–Markov theorem (brief...

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

categories include the five lemma (and the short five lemma as a special case), as well as the snake lemma (and the nine lemma as a special case). An...

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. The five lemma gives...

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...

In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally...

Lemma Guya Gemeda (1928–2020) (Oromo: Lammaa Guyyaa Gammadaa), was Ethiopian painter, airplane pilot, and author. He created some ten-thousand of his...

the map T {\displaystyle T} is forced to be an isomorphism by the short five lemma. It may happen that the extensions 1 → K → G → H → 1 {\displaystyle 1\to...

A commutative diagram depicting the five lemma...

extensions of A by B) if there is a commutative diagram: Note that the Five lemma implies that the middle arrow is an isomorphism. An extension of A by...

algebra homomorphism E → E' that induces the identities on I and R. By the five lemma, such a morphism is necessarily an isomorphism, and so two extensions...

lemma continent (epeiros), 5 continents model; Lexico Triantaphyllide online dictionary, Greek Language Center (Kentro Hellenikes Glossas), lemma continent...

In graph theory, a branch of mathematics, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch...

F(R^{\oplus n}).} The same thing holds for G {\displaystyle G} . Now apply the five lemma. ◻ {\displaystyle \square } Coherent module Finitely related module Fitting...

A basic fact about perfect groups is Otto Grün's proposition of Grün's lemma (Grün 1935, Satz 4, p. 3): the quotient of a perfect group by its center...

the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. This lemma is an intermediate step...

long exact sequences of homotopy groups, from which (by applying the Five Lemma, as is done in the Puppe sequence) one can see that the map F → Ff is...

In mathematics, Dickson's lemma states that every set of n {\displaystyle n} -tuples of natural numbers has finitely many minimal elements. This simple...

theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however...

the claim follows from the lemma. (In a nutshell, the lemma follows from the long exact homotopy sequence and the five lemma.) Davis, James F.; Kirk, Paul...