Some articles on exact, left exact, left:
Derived Functor - Naturality
... Derived functors and the long exact sequences are "natural" in several technical senses ... where the rows are exact), the two resulting long exact sequences are related by commuting squares Second, suppose η F → G is a natural transformation from ... indeed Ri becomes a functor from the functor category of all left exact functors from A to B to the full functor category of all functors from A to B ...
... Derived functors and the long exact sequences are "natural" in several technical senses ... where the rows are exact), the two resulting long exact sequences are related by commuting squares Second, suppose η F → G is a natural transformation from ... indeed Ri becomes a functor from the functor category of all left exact functors from A to B to the full functor category of all functors from A to B ...
Exact Functor - Properties and Theorems
... equivalence or duality of abelian categories is exact ... not necessarily additive) functor is left exact if and only if it turns finite limits into limits a covariant functor is right exact if and only if it turns finite colimits into ... A functor is exact if and only if it is both left exact and right exact ...
... equivalence or duality of abelian categories is exact ... not necessarily additive) functor is left exact if and only if it turns finite limits into limits a covariant functor is right exact if and only if it turns finite colimits into ... A functor is exact if and only if it is both left exact and right exact ...
Resolution (algebra) - Acyclic Resolution
... situations, the notion of acyclic resolutions is used given a left exact functor F A → B between two abelian categories, a resolution of an object M ... Dually, a left resolution is acyclic with respect to a right exact functor if its derived functors vanish on the objects of the resolution ... For example, given a R module M, the tensor product is a right exact functor Mod(R) → Mod(R) ...
... situations, the notion of acyclic resolutions is used given a left exact functor F A → B between two abelian categories, a resolution of an object M ... Dually, a left resolution is acyclic with respect to a right exact functor if its derived functors vanish on the objects of the resolution ... For example, given a R module M, the tensor product is a right exact functor Mod(R) → Mod(R) ...
Famous quotes containing the words exact and/or left:
“In the long-run every Government is the exact symbol of its People, with their wisdom and unwisdom; we have to say, Like People like Government.”
—Thomas Carlyle (1795–1881)
“Protestantism has the method of Jesus with His secret too much left out of mind; Catholicism has His secret with His method too much left out of mind; neither has His unerring balance, His intuition, His sweet reasonableness. But both have hold of a great truth, and get from it a great power.”
—Matthew Arnold (1822–1888)
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