Meanings
plural Cartesian closed categories
- category theoryA category which has a terminal object and which for every two objects A and B has a product A × B and an exponential object Bᴬ.
In any event, Lambek showed that every typed lambda-theory gives a cartesian closed category — and conversely, every cartesian closed category gives a typed lambda-theory. This discovery led to a rich line of research blending category theory and computer science.
2009 February 3, John C. Baez with Mike Stay, Physics, Topology, Logic and Computation: A Rosetta Stone, page 54Synonyms: CCC
Synonyms & antonyms
nounA category which has a terminal object and which for every two objects A and B has a product A × B and an exponential object Bᴬ.
Origin
Named after René Descartes (1596–1650), French philosopher, mathematician, and scientist, whose formulation of analytic geometry gave rise to the concept of Cartesian product, which was later generalized to the notion of categorical product.
Full word history & related roots →Cite this entry
Cartesian closed category. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Cartesian%20closed%20category
“Cartesian closed category.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Cartesian%20closed%20category. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “Cartesian closed category,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Cartesian%20closed%20category.
Source: Cartesian closed category on Wiktionary, CC BY-SA 4.0.