closed monoidal category
In mathematics, a closed monoidal category C is a closed category with an associative tensor product (up to
natural isomorphism) which is left
adjoint to the internal Hom functor, that is a monoidal category equipped with a functor ⇒ such that the functor
is right
adjoint to the functor 
. This means that there exists a bijection between the Hom-sets
natural in B and C.
Equivalently, a closed monoidal category C is a category equipped, for every two objects A and B, with
- an object A⇒B,
- a morphism
,
satisfying the following universal property: for every morphism
there exists a unique morphism
- h:X→A⇒B
such that
.
In particular, every cartesian closed category is a closed monoidal category.
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
