|
|
|
|
Ext functor
Ext functor In mathematics, the Ext functors of homological algebra are derived functors of Hom functors. They were first used in algebraic ...
http://en.wikipedia.org/wiki/Ext_functor - 1k - Cached - Similar pages
|
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 ...
http://en.wikipedia.org/wiki/Derived_functor - 15k - Cached - Similar pages
|
Group cohomology
... to study groups using a sequence of functors H n . Motivation A general paradigm in ... precisely measures the difference. The group cohomology functors H n in general measure the extent ... exact. We may therefore form its derived functors; their values are abelian groups and they ... Rather than using the machinery of derived functors, we can also define the cohomology groups ... over the group ring ZG and use Ext functors: H n (G,M) = Ext ...
http://en.wikipedia.org/wiki/Group_cohomology - 12k - Cached - Similar pages
|
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, ...
http://en.wikipedia.org/wiki/Derived_category - 5k - Cached - Similar pages
|
Injective sheaf
... to define sheaf cohomology (and other derived functors, such as sheaf Ext.). There is a further group of related ... 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 ... hoc means: for example, the left derived functors of Tor can be defined using ...
http://en.wikipedia.org/wiki/Injective_sheaf - 8k - Cached - Similar pages
|
Cohomology operation
... aspect is implicit in the use of Ext functors, the derived functors of Hom-functors; if there is a bicommutant aspect, taken ... G)\, is a natural transformation of functors |
Local cohomology
... in a closed subset Y. The derived functors of Γ Y form local cohomology groups ... local duality theorem, of Serre duality, using Ext functors of R-modules and a dualising module ...
http://en.wikipedia.org/wiki/Local_cohomology - 3k - Cached - Similar pages
|
Homological algebra
... derived functor; the most basic examples are Ext and Tor. Foundational aspects With a diverse ... needed, for instance, to compute the derived functors of a composition of two functors. Spectral sequences are less essential in the ...
http://en.wikipedia.org/wiki/Homological_algebra - 4k - Cached - Similar pages
|
User:Mathbot/List of mathematical redlinks (E)
... Equilogical spaces -- Equimorphism -- Equitable coloring -- Equivalence of functors -- Equivalent resistance -- Equivalent (semigroup theory) -- Equivalent set ... series -- EX Exportation (logic) -- Expr -- Expressive -- Expressiveness -- Ext functor of sheaves -- Extended Kalman filter -- Extending ...
http://en.wikipedia.org/wiki/User:Mathbot/List_of_mathematical_redlinks_(E) - 20k - Cached - Similar pages
|
Steenrod algebra
... operation is a natural transformation between cohomology functors. For example, if we take cohomology with ... sequence may be identified as |
| Page:1 2 Next >> |
