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. 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.[1]

  1. ^ Baez, John C.; Stay, Mike (2011). "Physics, Topology, Logic and Computation: A Rosetta Stone" (PDF). In Coecke, Bob (ed.). New Structures for Physics. Lecture Notes in Physics. Vol. 813. Springer. pp. 95–174. arXiv:0903.0340. CiteSeerX 10.1.1.296.1044. doi:10.1007/978-3-642-12821-9_2. ISBN 978-3-642-12821-9. S2CID 115169297.