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

B), for fixed A in ModR. This is a left exact functor and thus has right derived functors RnT. The Ext functor is defined by Ext R n ⁡ ( A , B ) = ( R...

a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an...

another left (resp. right) t-exact functor, then the composite G ∘ F {\displaystyle G\circ F} is also left (resp. right) t-exact. The motivation for the study...

different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and clarifies many of...

a functor is called left exact if it preserves all finite limits and right exact if it preserves all finite colimits. (A functor is simply exact if it's...

The concept of exact sequence arises naturally in this setting, and it turns out that exact functors, i.e. the functors preserving exact sequences in various...

Long exact sequences induced by short exact sequences are also characteristic of derived functors. Exact functors are functors that transform exact sequences...

In mathematics, the Landweber exact functor theorem, named after Peter Landweber, is a theorem in algebraic topology. It is known that a complex orientation...

relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in...

left exact (right exact, respectively) functor. The importance of acyclic resolutions lies in the fact that the derived functors RiF (of a left exact functor...

between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous applications in category...

In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological...

In mathematics, a topological half-exact functor F is a functor from a fixed topological category (for example CW complexes or pointed spaces) to an abelian...

mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central...

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

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

Comonad Combinatorial species Exact functor Derived functor Dominant functor Enriched functor Kan extension of a functor Hom functor Product (category theory)...

resolution Injective resolution Koszul complex Exact functor Derived functor Ext functor Tor functor Filtration (abstract algebra) Spectral sequence...

tensor product with a vector space is an exact functor; this means that every exact sequence is mapped to an exact sequence (tensor products of modules do...

derived functors of a left exact functor on an abelian category, while "homology" is used for the left derived functors of a right exact functor. For example...

the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X. The direct image functor is the primary operation...

This functor is always left exact, but, when P is projective, it is also right exact. This means that P is projective if and only if this functor preserves...

derived functors of a right exact functor (such as Tor). This can sometimes be done by ad hoc means: for example, the left derived functors of Tor can...

In mathematics, the direct image functor is a construction in sheaf theory that generalizes the global sections functor to the relative case. It is of fundamental...

can speak of an exact functor between exact categories exactly as in the case of exact functors of abelian categories: an exact functor F {\displaystyle...

Given a right exact functor F : A → B {\displaystyle F\colon {\mathcal {A}}\to {\mathcal {B}}} , one can define the left hyper-derived functors of F {\displaystyle...

and a full, faithful and exact functor F: A → R-Mod (where the latter denotes the category of all left R-modules). The functor F yields an equivalence...

objects from B {\displaystyle {\mathcal {B}}} . There is a canonical exact functor Q : A → A / B {\displaystyle Q\colon {\mathcal {A}}\to {\mathcal {A}}/{\mathcal...

in the category of modules is an exact functor. This means that if you start with a directed system of short exact sequences 0 → A i → B i → C i → 0...