closed monoidal category
is right closed if the functor on has a right adjoint
is biclosed if it is both left closed and right closed.
Any cartesian closed category is symmetric monoidal closed.
An example of a biclosed monoidal category that is not symmetric monoidal is the category of bimodules over a non-commutative ring. The right adjoint of is , where is the collection of all left -linear bimodule homomorphisms from to , while the right adjoint of is , where is the collection of all right -linear bimodule homomorphisms from to . Unless is commutative, in general.
more to come…
|Title||closed monoidal category|
|Date of creation||2013-03-22 18:30:25|
|Last modified on||2013-03-22 18:30:25|
|Last modified by||CWoo (3771)|
|Defines||symmetric monoidal closed|