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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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 ... and by Mod-R the category of right R-modules (if R is commutative, the ... A⊗ R B. Then T is a right exact functor from Mod-R to the ...
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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 functors $R^nT$). To ...
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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 ... left adjoint to G, and G is right adjoint to F. Since G may have itself a right adjoint, quite different from F (see ...
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Talk:Function (mathematics)
... x loves y)is called "intension" (or functor) of R [Dea93]. x and y can ... and they are the arguments of the functor. Each pair of ordered values (Romeo,Juliet ... At the moment of the substitution, the functor became a proposition; which, in turns, can ... Also, rather than (or: before) citing "operators" right here, I think a link to partial ... thought ordered groups doesn't sound quite right, but ordered pairs would not cover ...
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Pre-Abelian category
... is the coimage, the morphism on the right is the image, and the morphism in ... 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 ...
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User talk:Trovatore/Archive02
... there is no consensus that he was right, Frapolli arguing that Cantor's view was ... gentle kick in the pants. You're right; I should cut way back on WP ... kick in the pants can be gentle. Right about WP though. I am also attempting ... I talked to you properly, on the right page, in the right way. Anyway, I need some guidance ...
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Talk:Manifold/rewrite/freezer
... the examples are discussed in the section right below. Oleg Alexandrov 2 July 2005 05 ... good point, and thanks for not reverting right away. I think it is good to have that example, but not right in the definition. The problem is the ... 23 (UTC) Yes, you got my point right. But I don't find your suggestion ... and Antarctica is unnecessary. That is explained right below, in the circle manifold example ...
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Flat module
... tensor product over R with M preserves exact sequences. Vector spaces over a field are ... to tensor product with M being an exact functor from the category of R-modules to ... module) the tensor product with M maps exact sequences of right R-modules to exact sequences of ...
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