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Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry.

The modern Cartesiancoordinate system in two dimensions (also called a rectangular coordinate system) is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane).

In analytic geometry the Cartesiancoordinate system is the foundation for the algebraic manipulation of geometrical shapes.

The category of all directed graphs is cartesian closed; this is a functor category as explained under functor category.

In algebraic topology, cartesian closed categories are particularly easy to work with, and it is regrettable that neither the category of topological spaces with continuous maps nor the category of smooth manifolds with smooth maps is cartesian closed.

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

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