An exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category)...

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...

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...

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...

mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations...

spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and...

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...

< 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 (...

spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and...

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...

Therefore, ASVs represent a finer distinction between sequences. ASVs are also referred to as exact sequence variants (ESVs), zero-radius OTUs (ZOTUs), sub-OTUs...

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...

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...

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...

short exact sequences exact after tensoring, a pure submodule defines a short exact sequence (known as a pure exact sequence) that remains exact after...

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...

(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...

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...

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...

inflation-restriction exact sequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge...

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...

{\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 ) →...

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...

In mathematics, exactness may refer to: Exact category Exact functor Landweber exact functor theorem Exact sequence Exactness of measurements Accuracy...

statement: If 0 → K → P → M → 0 and 0 → K′ → P′ → M → 0 are short exact sequences of R-modules and P and P′ are projective, then K ⊕ P′ is isomorphic...

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...

in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial...

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;...

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...

research Exact colorings, in graph theory Exact couples, a general source of spectral sequences Exact sequences, in homological algebra Exact functor,...