Cartesian Monoidal Category

(Category Theory)


Category Theory
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What is Cartesian monoidal category?

In mathematics, specifically in the field known as category theory, a monoidal category where the monoidal ("tensor") product is the categorical product is called a cartesian monoidal category. Any category with finite products (a "finite product category") can be thought of as a cartesian monoidal category. In any cartesian monoidal category, the terminal object is the tensor unit. Dually, a monoidal finite coproduct category with the monoidal structure given by the coproduct and unit the initial object is called a cocartesian monoidal category, and any finite coproduct category can be thought of as a cocartesian monoidal category. Cartesian categories with an internal Hom functor that is an adjoint functor to the product are called Cartesian closed categories.

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category theorymonoidal category


Cocartesian monoidal category


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