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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 ... to Mod-R) and its left derived functors L n T are defined. We ...
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Tor (disambiguation)
Tor (disambiguation) Toronto, Ontario A tor is a high craggy hill. This term ... referring to the high points of Dartmoor. Tor (port) is the name of a port ... on the Sinai peninsula. In Norse mythology, Tor is the Scandinavian form of the god Thor. In biology, Tor is the genus of the mahseers, ...
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Derived functor
Derived functor In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This ... long exact sequence". The concept of derived functors explains and clarifies many of these observations ... doing so, given by the right derived functors of F. For every i≥1, there is ... so in a sense the right derived functors of F measure "how far" F ...
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Flat module
... direct sums and direct limits are exact functors. Submodules and factor modules of flat modules ... Flatness may also be expressed using the Tor functors, the left derived functors of the tensor product. A left R ... M is flat if and only if Tor 1 R (–, M) = 0 (i. ...
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Derived category
... sense to simplify the theory of derived functors defined on C (which therefore should already ... established Cartan-Eilenberg method of accepting derived functors such as the Tor functors and Ext functors as natural.) In coherent sheaf theory, ...
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Injective sheaf
... to define sheaf cohomology (and other derived functors, such as sheaf Ext.). There is a ... is enough to show that right derived functors of any left exact functor exist and ... problems when attempting to define left derived functors of a right exact functor (such as Tor). This can sometimes be done by ad ... hoc means: for example, the left derived functors of Tor can be defined using ...
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Künneth theorem
... of homological algebra, namely use of the Tor functors. From now on the coefficients in R ... there is no need to invoke the Tor functors. The result in this case can be ... T by the direct sum of the Tor R (H p (X), H q ( ...
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User talk:AxelBoldt/Archive
... if you can make it to adjoint functors, you will know more about categories than ... 21:29, 8 Aug 2004 (UTC) Re: Tor functor. I see you have undone some ... allow natural transformations between covariant and contravariant functors? One just need to reverse the appropriate ... for two covariant or for two contravariant functors. One problem may be that the inverse ... of natural transformation between covariant and contravariant functors defined somewhere? If not, then I ...
http://en.wikipedia.org/wiki/User_talk:AxelBoldt/Archive - 255k - Cached - Similar pages
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Homology (mathematics)
... algebra, one uses homology to define derived functors, for example the Tor functors. Here one starts with some covariant additive ... math>, applied to . Homology functors Chain complexes form a category: A morphism ... then the are covariant functors from the category that |
Torsion (abstract algebra)
... that of a torsion module.) In the Tor functors of homological algebra, which arise because tensor ... in general preserve exact sequences, the symbol Tor does stand for this kind of algebraic torsion, historically speaking anyway. These functors were introduced in order to make systematic ...
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