Exact functor
Exact functor In homological algebra, an exact functor is one which preserves exact sequences. Formally, let C and D ...
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Talk:Exact functor
Talk:Exact functor Isn't it necessary that exact functors between abelian categories are additive? Otherwise ...
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Functor
Functor For functors in computer science, see the ... function object article. In category theory, a functor is a special type of mapping between ... Let C and D be categories. A functor F from C to D is a ... reverse composition". We then define a contravariant functor F from C to D as a ... that one can also define a contravariant functor as a covariant functor on the ...
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Derived functor
Derived functor In mathematics, certain functors may be derived ... various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains ... Suppose we are given a covariant left exact functor F : A → B between two ...
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Tor functor
Tor functor In mathematics, the Tor functors of homological ... the derived functors of the tensor product functor. They were first defined in generality to ... R B. Then T is a right exact functor from Mod-R to the category of ... R is commutative, it is a right exact functor from Mod-R to Mod- ...
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Ext functor
Ext functor In mathematics, the Ext functors of homological ... mathcal C. (This is a left exact functor (contravariant) so we want its right derived ...
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Image:Two long exact sequences2.png
Image:Two long exact sequences2.png Image File history File links Two_long_exact_sequences2.png Image of two long exact sequences, to be used for derived functor. Produced with Xy-pic using the following ...
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Adjoint functors
... adjoint functors The idea of an adjoint functor was formulated by Daniel Kan in 1958 ... of abelian groups, where F was the functor –⊗A (i.e. take the tensor product with A), and G was the functor Hom(A,–). The use of the ... By itself, the generality of the adjoint functor concept isn't a recommendation to most ... to say that he promoted the adjoint functor concept in isolation: but recognition of ...
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Pre-Abelian category
... isomorphism unless the range was already closed. Exact functors Recall that all finite limits and ... Abelian category. In general category theory, 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 ...
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List of mathematics articles (D-F)
... Derivative of a constant -- Derived category -- Derived functor -- Derived group -- Derived set (mathematics) -- Desargues' theorem ... space -- Dirac measure -- Dirac operator -- Direct image functor -- Direct integral -- Direct limit -- Direct product -- Direct ... Enneagon -- Enneper-Weierstrass parameterization -- Enriched category -- Enriched functor -- Enriques-Kodaira classification -- Enriques surface -- Entire function ... Evolutionary graph theory -- Ewens's sampling formula -- Exact coloring -- Exact differential -- Exact functor -- Exact sequence -- Exact ...
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