diagram lemma
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diagram chasing — noun Proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms. To prove the five lemma, just use diagram chasing. See Also: diagram chase … Wiktionary
diagram chase — noun A proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms. To prove the five lemma, just use a diagram chase. See Also: diagram chasing … Wiktionary
Five lemma — In mathematics, especially homological algebra and other applications of Abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams.The five lemma is valid not only for abelian categories but also… … Wikipedia
Van Kampen diagram — In the mathematical area of geometric group theory, a van Kampen diagram is a planar diagram used to represent the fact that a particular word among the generators of a group given by a group presentation represents the identity element in that… … Wikipedia
Snake lemma — 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 and is a crucial tool in homological algebra and its applications, for instance … Wikipedia
Commutative diagram — For help on drawing commutative diagrams on Wikipedia, see meta:Help:Displaying a formula#Commutative diagrams. In mathematics, and especially in category theory, a commutative diagram is a diagram of objects (also known as vertices) and… … Wikipedia
Yoneda lemma — In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object . It is a vast generalisation of Cayley s theorem from group theory (a group being a particular kind of… … Wikipedia
Horseshoe lemma — In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects A and A to resolutions ofextensions of A by A . It says that if an object A is an extension of A by A … Wikipedia
Zig-zag lemma — In mathematics, particularly homological algebra, the zig zag lemma asserts the existence of a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category. Statement In an… … Wikipedia
Nine lemma — In mathematics, the nine lemma is a statement about commutative diagrams and exact sequences valid in any abelian category, as well as in the category of groups. It states: if is a commutative diagram and all columns as well as the two bottom… … Wikipedia
Cluster diagram — A Cluster diagram or clustering diagram is a general type of diagram, which represents some kind of cluster. A cluster in general is a group or bunch of several discrete items that are close to each other. [1] The cluster diagram figures a… … Wikipedia
