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 the category of sets, this is an object of the category itself. In the same vein, in a closed category, the (object of) morphisms from one object to another can be seen as lying inside the category. This is the internal hom [x, y]. Every closed category has a forgetful functor to the category of sets, which in particular takes the internal hom to the external hom. (Wikipedia).

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From playlist Calculus

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From playlist Middle School This Year

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From playlist Course 6: Introduction to Analysis (Fall 2017)

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From playlist Topology

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Category of sets | Dinatural transformation | Forgetful functor | Cartesian closed category | Mathematics | Set (mathematics) | Topos | Compact closed category | Category theory | Category (mathematics) | Natural transformation