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In mathematics, the nine lemma (or 3×3 lemma) is a statement about commutative diagrams and exact sequences valid in the category of groups and any abelian...

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

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 categories...

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

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...

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

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 abelian...

S ∩ N is the meet. The third isomorphism theorem is generalized by the nine lemma to abelian categories and more general maps between objects. Below we...

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...

In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects A ′ {\displaystyle...

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 mathematical queueing theory, Little's law (also result, theorem, lemma, or formula) is a theorem by John Little which states that the long-term average...

establish the theorem, Thâbit ibn Qurra proved nine lemmas divided into two groups. The first three lemmas deal with the determination of the aliquot parts...

In geometry, the incenter–excenter lemma is the theorem that the line segment between the incenter and any excenter of a triangle, or between two excenters...

Retrieved 20 December 2010. "Failure to shoot straight derails Iemma". nineMSN. Archived from the original on 3 December 2007. "Anger good, swearing...

for specialist mathematicians to grasp. To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental...

internal surfaces. A consequence of Cauchy's postulate is Cauchy's Fundamental Lemma, also called the Cauchy reciprocal theorem,: p.103–130  which states that...

ended their rivalry and performed together on the same stage. "Kill Dash Nine" (appears on Rhyme Torrents Vol.1) Daniel "Monzy" Aminzade also created a...

Archived from the original on 14 June 2021. Retrieved 6 April 2021. Lemma B.2.2, The integer 0 is even and is not odd, in Penner, Robert C. (1999)...