Cartesian closed category

English

Etymology

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.

Noun

Cartesian closed category (plural Cartesian closed categories)

1. (category theory) 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 B^A.
   • 2009 March 2, John C. Baez with Mike Stay, Physics, Topology, Logic and Computation: A Rosetta Stone‎^[1], page 54:

     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.

Synonyms

• CCC

Hypernyms

• Cartesian monoidal category, Cartesian category
• closed monoidal category
• monoidal category

Hyponyms

• bicartesian closed category
• topos