# Category: Closed categories

Closed category
In category theory, a branch of mathematics, a closed category is a special kind of category. In a locally small category, the external hom (x, y) maps a pair of objects to a set of morphisms. So in t
Closed monoidal category
In mathematics, especially in category theory, a closed monoidal category (or a monoidal closed category) is a category that is both a monoidal category and a closed category in such a way that the st
Cartesian closed category
In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. The
*-autonomous category
In mathematics, a *-autonomous (read "star-autonomous") category C is a symmetric monoidal closed category equipped with a dualizing object . The concept is also referred to as Grothendieck—Verdier ca
Compact closed category
In category theory, a branch of mathematics, compact closed categories are a general context for treating dual objects. The idea of a dual object generalizes the more familiar concept of the dual of a