What is "cartesian closed category"

n. (context category theory English) A category which has a terminal object and which for every two objects ''A'' and ''B'' has a product ''A'' × ''B'' and an exponential object ''B''^''A''.

In category theory, a category is considered 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. These categories are particularly important in mathematical logic and the theory of programming, in that their internal language is the simply typed lambda calculus. They are generalized by closed monoidal categories, whose internal language, linear type systems, are suitable for both quantum and classical computation.