An exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category)...
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split exact sequence is a short exact sequence in which the middle term is built out of the two outer terms in the simplest possible way. A short exact sequence...
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Homological algebra (redirect from Long exact sequence in homology)
and cokernels. The most common type of exact sequence is the short exact sequence. This is an exact sequence of the form A ↪ f B ↠ g C {\displaystyle...
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mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations...
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spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and...
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Homotopy group (redirect from Exact sequence of a fibration)
cofibration is the mapping cone, then the resulting exact (or dually, coexact) sequence is given by the Puppe sequence. There are many realizations of spheres as...
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Fibration (redirect from Fibration sequence)
< q < n {\displaystyle 0<q<n} hold, an exact sequence exists (also known under the name Serre exact sequence): H m + n − 1 ( F ) → i ∗ H m + n − 1 (...
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inflation-restriction exact sequence is an exact sequence occurring in group cohomology and is a special case of the five-term exact sequence arising from the...
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In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in...
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spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and...
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Pure submodule (redirect from Pure exact sequence)
short exact sequences exact after tensoring, a pure submodule defines a short exact sequence (known as a pure exact sequence) that remains exact after...
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compute. The sequence relates the (co)homology groups of the space to the (co)homology groups of the subspaces. It is a natural long exact sequence, whose entries...
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Therefore, ASVs represent a finer distinction between sequences. ASVs are also referred to as exact sequence variants (ESVs), zero-radius OTUs (ZOTUs), sub-OTUs...
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mathematics, the Puppe sequence is a construction of homotopy theory, so named after Dieter Puppe. It comes in two forms: a long exact sequence, built from the...
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Module homomorphism (section Exact sequences)
(f_{i+1})=\operatorname {ker} (f_{i})} . A special case of an exact sequence is a short exact sequence: 0 → A → f B → g C → 0 {\displaystyle 0\to A{\overset {f}{\to...
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surgery exact sequence is the long exact sequence induced by a fibration sequence of spectra. This implies that all the sets involved in the sequence are...
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Chain complex (section Exact sequences)
An exact sequence (or exact complex) is a chain complex whose homology groups are all zero. This means all closed elements in the complex are exact. A...
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mathematics, five-term exact sequence or exact sequence of low-degree terms is a sequence of terms related to the first step of a spectral sequence. More precisely...
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Projective module (section Split-exact sequences)
short exact sequence of modules of the form 0 → A → B → P → 0 {\displaystyle 0\rightarrow A\rightarrow B\rightarrow P\rightarrow 0} is a split exact sequence...
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In mathematics, the Euler sequence is a particular exact sequence of sheaves on n-dimensional projective space over a ring. It shows that the sheaf of...
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Category of groups (section Exact sequences)
finite field has for its order, the power of a prime. The notion of exact sequence is meaningful in Grp, and some results from the theory of abelian categories...
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In mathematics, exactness may refer to: Exact category Exact functor Landweber exact functor theorem Exact sequence Exactness of measurements Accuracy...
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{\displaystyle \Longrightarrow } ' means convergence of spectral sequences. The exact sequence of low degrees reads 0 → R 1 G ( F A ) → R 1 ( G F ) ( A ) →...
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only if O K {\displaystyle {\mathcal {O}}_{K}} is a UFD. There is an exact sequence 0 → O K ∗ → K ∗ → I K → C K → 0 {\displaystyle 0\to {\mathcal {O}}_{K}^{*}\to...
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inflation-restriction exact sequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge...
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Gysin homomorphism (redirect from Gysin exact sequence)
field of mathematics known as algebraic topology, the Gysin sequence is a long exact sequence which relates the cohomology classes of the base space, the...
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In mathematics, an exact couple, due to William S. Massey (1952), is a general source of spectral sequences. It is common especially in algebraic topology;...
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Splitting lemma (redirect from Splitting sequence)
holds, the sequence is called a split exact sequence, and the sequence is said to split. In the above short exact sequence, where the sequence splits, it...
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In mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry. Let M be a complex manifold,...
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research Exact colorings, in graph theory Exact couples, a general source of spectral sequences Exact sequences, in homological algebra Exact functor,...
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