Sequence of homomorphisms such that each kernel equals the preceding image
Illustration of an exact sequence of groups using Euler diagrams.
An exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category) such that the image of one morphism equals the kernel of the next.
An exactsequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category)...
split exactsequence is a short exactsequence in which the middle term is built out of the two outer terms in the simplest possible way. A short exact sequence...
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 exactsequences. 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 exactsequences, and...
inflation-restriction exactsequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge...
spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exactsequences, and...
Therefore, ASVs represent a finer distinction between sequences. ASVs are also referred to as exactsequence variants (ESVs), zero-radius OTUs (ZOTUs), sub-OTUs...
In the mathematical surgery theory the surgery exactsequence is the main technical tool to calculate the surgery structure set of a compact manifold in...
An exactsequence (or exact complex) is a chain complex whose homology groups are all zero. This means all closed elements in the complex are exact. A...
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;...
mathematics, the Puppe sequence is a construction of homotopy theory, so named after Dieter Puppe. It comes in two forms: a long exactsequence, built from the...
(f_{i+1})=\operatorname {ker} (f_{i})} . A special case of an exactsequence is a short exactsequence: 0 → A → f B → g C → 0 {\displaystyle 0\to A{\overset {f}{\to...
surgery exactsequence is the long exactsequence induced by a fibration sequence of spectra. This implies that all the sets involved in the sequence are...
In mathematics, the Euler sequence is a particular exactsequence of sheaves on n-dimensional projective space over a ring. It shows that the sheaf of...
research Exact colorings, in graph theory Exact couples, a general source of spectral sequencesExactsequences, in homological algebra Exact functor,...
short exactsequence 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...
{\displaystyle \Longrightarrow } ' means convergence of spectral sequences. The exactsequence of low degrees reads 0 → R 1 G ( F A ) → R 1 ( G F ) ( A ) →...
field of mathematics known as algebraic topology, the Gysin sequence is a long exactsequence which relates the cohomology classes of the base space, the...
only if O K {\displaystyle {\mathcal {O}}_{K}} is a UFD. There is an exactsequence 0 → O K ∗ → K ∗ → I K → C K → 0 {\displaystyle 0\to {\mathcal {O}}_{K}^{*}\to...
holds, the sequence is called a split exactsequence, and the sequence is said to split. In the above short exactsequence, where the sequence splits, it...
in mathematics, particularly homological algebra, to construct long exactsequences. The snake lemma is valid in every abelian category and is a crucial...
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