Exact functor information

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...

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...

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...

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

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

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, 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...

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

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

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...

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

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...

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

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...

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...

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...

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...

yields a functor from the category of G-modules to the category Ab of abelian groups. This functor is left exact but not necessarily right exact. We may...

homology theory as a functor that takes spaces to long-exact sequences of groups. It is also useful as a tool to build long exact sequences of relative...

suspension theorem (a corollary of the excision theorem) Landweber exact functor theorem Dold–Kan correspondence Eckmann–Hilton argument - this shows...