tensor-hom adjunction is that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ( X , − ) {\displaystyle \operatorname {Hom}...
5 KB (912 words) - 14:09, 13 June 2024
Adjoint functors (redirect from Unit of adjunction)
functors F : D → C, G : C → D, and a hom-set adjunction Φ : homC(F-,-) → homD(-,G-), one can construct a counit–unit adjunction ( ε , η ) : F ⊣ G {\displaystyle...
63 KB (9,958 words) - 21:43, 1 August 2024
Natural transformation (section Tensor-hom adjunction)
functor on Ab {\displaystyle {\textbf {Ab}}} !) This is formally the tensor-hom adjunction, and is an archetypal example of a pair of adjoint functors. Natural...
33 KB (5,663 words) - 12:43, 25 June 2024
_{R}N,G)\simeq \operatorname {Hom} _{R}(M,\operatorname {Hom} _{\mathbb {Z} }(N,G)).} This is known as the tensor-hom adjunction; see also § Properties. For...
48 KB (8,467 words) - 22:58, 6 April 2024
covectors α, β. Such a nonsingular symmetric mapping gives rise (by the tensor-hom adjunction) to a map T ∗ M ⊗ T ∗ M → R {\displaystyle \mathrm {T} ^{*}M\otimes...
56 KB (8,866 words) - 08:52, 9 August 2024
currying and uncurrying is known as tensor-hom adjunction. Here, an interesting twist arises: the Hom functor and the tensor product functor might not lift...
36 KB (5,016 words) - 01:30, 27 August 2024
Monad (category theory) (redirect from Monadic adjunction)
mentioned above, any adjunction gives rise to a monad. Conversely, every monad arises from some adjunction, namely the free–forgetful adjunction T ( − ) : C ⇄...
30 KB (4,467 words) - 15:23, 8 August 2024
the restriction of scalars functor. Six operations Tensor product of fields Tensor-hom adjunction Dummit, David (2004). Abstract algebra. Foote, Richard...
9 KB (1,549 words) - 15:26, 16 February 2024
homological algebra, the adjointness of curry and apply is known as tensor-hom adjunction. In order theory, in the category of complete partial orders endowed...
12 KB (1,449 words) - 01:00, 28 June 2023
where 1 is the one-point set. Because of this, and the adjunction between Cartesian products and hom in the category of sets (so there is a canonical isomorphism...
8 KB (985 words) - 02:18, 3 April 2024