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Tor functor
Tor functor In mathematics, the Tor functors of homological algebra are the derived functors of the tensor product functor. They were first defined in generality to ... B. Then T is a right exact functor from Mod-R to the category ...
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Talk:Tor functor
Talk:Tor functor could someone give an indication about where ... There seems to be no mathematician named "Tor". — MFH:Talk 12:56, 21 February ...
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Derived functor
Derived functor In mathematics, certain functors may be derived ... we are given a covariant left exact functor F : A → B between two abelian ... F. For every i≥1, there is a functor R i F: A → B, and ... we see that F is an exact functor if and only if R 1 F ... injective, then the sequence splits. Applying a functor to a split sequence results in ...
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Flat module
... tensor product with M being an exact functor from the category of R-modules to ... arbitrary rings) is always a right exact functor. Therefore, the R-module M is flat ... Flatness may also be expressed using the Tor functors, the left derived functors of the ... M is flat if and only if Tor 1 R (–, M) = 0 (i.e., iff Tor 1 R (X, M) = 0 for ...
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User talk:AxelBoldt/Archive
... 21:29, 8 Aug 2004 (UTC) Re: Tor functor. I see you have undone some of ... V* can be made into a (contravariant) functor. If f : V → W is a ... F : C → D is a covariant functor and G : C → D is a contravariant functor. Taking η a and η b ...
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Universal coefficient theorem
... used, at the cost of using a Tor functor. For example it is common to take ... theorem describes the cokernel of ι as Tor(H i − 1 ,A). This Tor group can therefore be described as the ... coefficient theorem for cohomology, involving the Ext functor.
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List of homological algebra topics
... Projective resolution Injective resolution Koszul complex Exact functor Derived functor Ext functor Tor functor Filtration (abstract algebra) Spectral sequence Abelian ...
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Category:Homological algebra
... De Rham-Weil theorem Derived category Derived functor Diagram chasing E Étale cohomology Exact functor Exact sequence Ext functor F Five lemma Flat module G Galois ... Splitting lemma T Tensor product of modules Tor functor Triangulated category U Universal coefficient theorem ...
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Homology (mathematics)
... to define derived functors, for example the Tor functors. Here one starts with some covariant additive functor and some module |
Injective sheaf
... right derived functors of any left exact functor exist and are unique up to canonical ... left derived functors of a right exact functor (such as Tor). This can sometimes be done by ad ... for example, the left derived functors of Tor can be defined using a flat resolution ...
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