tensor-hom adjunction is that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ⁡ ( X , − ) {\displaystyle \operatorname {Hom}...

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...

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...

_{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...

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...

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...

mentioned above, any adjunction gives rise to a monad. Conversely, every monad arises from some adjunction, namely the free–forgetful adjunction T ( − ) : C ⇄...

the restriction of scalars functor. Six operations Tensor product of fields Tensor-hom adjunction Dummit, David (2004). Abstract algebra. Foote, Richard...

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...

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...