Closed monoidal category

In mathematics, especially in category theory, a closed monoidal category (also called a monoidal closed category) is a context where it is possible both to form tensor products of objects and to form 'mapping objects'. A classic example is the category of sets, Set, where the tensor product of sets ${\displaystyle A}$ and ${\displaystyle B}$ is the usual cartesian product ${\displaystyle A\times B}$, and the mapping object ${\displaystyle B^{A}}$ is the set of functions from ${\displaystyle A}$ to ${\displaystyle B}$. Another example is the category FdVect, consisting of finite-dimensional vector spaces and linear maps. Here the tensor product is the usual tensor product of vector spaces, and the mapping object is the vector space of linear maps from one vector space to another.

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