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

The term split exact sequence is used in two different ways by different people. Some people mean a short exact sequence that right-splits (thus corresponding...

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...

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

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

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...

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...

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...

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...

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...

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;...

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...

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...

In mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry. Let M be a complex manifold,...

mathematics, specifically in category theory, an exact category is a category equipped with short exact sequences. The concept is due to Daniel Quillen and is...

extension of Q {\displaystyle Q} by N {\displaystyle N} if there is a short exact sequence 1 → N → ι G → π Q → 1. {\displaystyle 1\to N\;{\overset {\iota }{\to...

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...

extent to which taking invariants doesn't respect exact sequences. This is expressed by a long exact sequence. The collection of all G-modules is a category...

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...

C} is said to be exact if image  ψ = ker ⁡ φ {\displaystyle {\text{image }}\psi =\ker \varphi } . An exact sequence is then a sequence of modules and homomorphism...

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

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

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...

(or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of objects of an abelian category) that...

triangles generalize the short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology. Much of homological...

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