Cartesian Monoidal Category

(Category Theory)

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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.

Technology Types

category theorymonoidal category

Synonyms

Cocartesian monoidal category

Translations

デカルトモノイド圏 (ja)

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