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Cartesian closed category

Cartesian closed category noun: 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 Bᴬ.

Noun

Cartesian closed category (plural Cartesian closed categories)

  1. 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 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 54
    Synonyms:
    CCC

Synonyms of Cartesian closed category

Forms of Cartesian closed category

pluralCartesian closed categories

Origin of Cartesian closed category

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.

Questions about Cartesian closed category

What does Cartesian closed category mean?
Cartesian closed category means 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 Bᴬ.
What part of speech is Cartesian closed category?
Cartesian closed category is a noun.
What is the plural of Cartesian closed category?
The plural of Cartesian closed category is Cartesian closed categories.

Words near Cartesian closed category in the dictionary

  1. cartes de visite
  2. cartesian
  3. Cartesian circle
  4. Cartesian circles
  5. Cartesian closed categories
  6. Cartesian closed category
  7. Cartesian coordinate
  8. cartesian coordinates
  9. Cartesian devil
  10. Cartesian devils
  11. cartesian distance

Source and license

Adapted from Wiktionary: Cartesian closed category (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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