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searching for Hom functor 9 found (48 total)

Symmetric monoidal category (631 words) [view diff] no match in snippet view article find links to article

\circledast } ) is a closed symmetric monoidal category with the internal hom-functor ⊘ {\displaystyle \oslash } . The classifying space (geometric realization

Mitchell's embedding theorem (655 words) [view diff] no match in snippet view article find links to article

A\in {\mathcal {A}}} , where h A {\displaystyle h^{A}} is the covariant hom-functor, h A ( X ) = Hom A ⁡ ( A , X ) {\displaystyle h^{A}(X)=\operatorname

Profunctor (952 words) [view diff] no match in snippet view article find links to article

) The previous definition can be recovered by the restriction of the hom-functor ϕ op × ϕ → S e t {\displaystyle \phi ^{\text{op}}\times \phi \to \mathbf

Dual object (1,037 words) [view diff] exact match in snippet view article find links to article

closed monoidal category C, i.e. a monoidal category with an internal Hom functor, an alternative approach is to simulate the standard definition of a

Six operations (1,049 words) [view diff] exact match in snippet view article find links to article

abelian sheaves, there is a tensor product functor ⊗ and an internal Hom functor, and these are adjoint. The six operations are the corresponding functors

Monoidal category (2,433 words) [view diff] no match in snippet view article find links to article

X\mapsto X\otimes A} has a right adjoint, which is called the "internal Hom-functor" X ↦ H o m C ( A , X ) {\displaystyle X\mapsto \mathrm {Hom} _{\mathbf

Commutative ring (5,688 words) [view diff] no match in snippet view article find links to article

map M → E. The higher Ext functors measure the non-exactness of the Hom-functor. The importance of this standard construction in homological algebra

Cohomology (7,044 words) [view diff] exact match in snippet view article find links to article

"cohomology theory" in each variable, the right derived functors of the Hom functor HomR(M,N). Sheaf cohomology can be identified with a type of Ext group

Glossary of commutative algebra (9,767 words) [view diff] exact match in snippet view article find links to article

form a closed subset. Ext The Ext functors, the derived functors of the Hom functor. extension 1. An extension of an ideal is the ideal generated by the