The articles on exponential object and Cartesian closed category provide a more precise discussion of the category-theoretic formulation of this idea.

More precisely, there exist functors between the category of Cartesian closed categories, and the category of simply-typed lambda theories.

This example is a Cartesian closed category.

Cartesian closed categories are closed categories.

Such a category is sometimes called a cartesian monoidal category.

Certain cartesian closed categories, the topoi, have been proposed as a general setting for mathematics, instead of traditional set theory.

CAML is more consciously modelled on cartesian closed categories.

One may ask what other such equations are valid in all cartesian closed categories.

This same construction defines weak NNOs in cartesian categories that are not cartesian closed.

Suppose is a cartesian category, product functors have been chosen as above, and denotes the terminal object of .