Ext functor
Ext functor In mathematics, the Ext functors of homological algebra are derived functors ... C. (This is a left exact functor (contravariant) so we want its right derived ... math>). To this end, define $\backslash operatorname\{$Ext}_R^n(A,B)=(R^nT)( ...
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Ext
Ext Ext or ext may refer to: ext, the extended file system the Ext functor in homological algebra Et cetera, ...
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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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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 ... sampling formula -- Exact coloring -- Exact differential -- Exact functor -- Exact sequence -- Exact trigonometric constants -- Examples of ... squaring -- Expression -- Expression (mathematics) -- EXPSPACE -- EXPTIME -- Exsecant -- Ext functor -- Extended Euclidean algorithm -- Extended number -- ...
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Coherent duality
... the continuing consideration of this area. Adjoint functor point of view While Serre duality uses ... as the existence of a right adjoint functor $f^!\backslash ;,$ now called twisted inverse ... a higher direct image with proper support functor $Rf\_!\backslash ;.$ Higher direct images are ... they are bundled up into a single functor by means of the derived category formulation ... a right adjoint, to the inverse image functor f * . The existence theorem for the ...
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Group cohomology
... group of invariants M G yields a functor from this category to the category Ab of abelian groups. This functor is left exact. We may therefore form ... over the group ring ZG and use Ext functors: H n (G,M) = Ext n ZG (Z,M). Here Z is ... of G acts as the identity. These Ext groups can also be computed via ...
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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 ... lemma T Tensor product of modules Tor functor Triangulated category U Universal coefficient theorem ...
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List of mathematics articles (E)
... Enneagon -- Enneper-Weierstrass parameterization -- Enriched category -- Enriched functor -- Enriques-Kodaira classification -- Enriques surface -- Entire function ... sampling formula -- Exact coloring -- Exact differential -- Exact functor -- Exact sequence -- Exact trigonometric constants -- Examples of ... squaring -- Expression -- Expression (mathematics) -- EXPSPACE -- EXPTIME -- Exsecant -- Ext functor -- Extended Euclidean algorithm -- Extended number -- Extended real ...
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User:Mathbot/List of mathematical redlinks (E)
... Essentially algebraic category -- Essentially small -- Essentially surjective functor -- Estagel -- Estermann -- Estienne Noel -- Estimation lemma -- Estonian ... series -- EX Exportation (logic) -- Expr -- Expressive -- Expressiveness -- Ext functor of sheaves -- Extended Kalman filter -- Extending scalar ...
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