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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…

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Overview

Etymology

Definition

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Examples

Applications

Dependent sum and product

Equational theory

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Map overview Semantic statistics

Cartesian closed category

Nodes94
Edges93
Triples56
Avg. degree1.98
Density0.021277
Components1

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Cartesian closed category

Top relations

related to Examples · 29
Cartesian closed category → An, Both, Cartesian, Cat, CD, Even, Examples, FG, Frölicher, G-sets, Hausdorff, Heyting, Hom, However, If, In, Indeed, Neither, Scott, Set
related to Dependent sum and product · 8
Cartesian closed category → C/X, C/Y, C/Z, Cartesian, For, Let, Taking, Then
has application · 7
Cartesian closed category → Cartesian, Howard, In, In Cartesian, Lambek, The Curry, ZY
related to External links · 7
Cartesian closed category → Cartesian, Category Café, CCCs, John, Texas, The, University
related to Equational theory · 5
Cartesian closed category → Cartesian, In, We, XY, XZ

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Important terminology

closed cartesian category categories product displaystyle functor object exponential objects set natural right adjoint locally two theory morphism morphisms times

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cartesian closed categoryhas applicationIn Cartesian0.60section
Cartesian closed categoryhas applicationZY0.60section
Cartesian closed categoryhas applicationIn0.60section
Cartesian closed categoryhas applicationCartesian0.60section
Cartesian closed categoryhas applicationThe Curry0.60section
Cartesian closed categoryhas applicationHoward0.60section
Cartesian closed categoryhas applicationLambek0.60section
Cartesian closed categoryrelated to Dependent sum and productLet0.60section
Cartesian closed categoryrelated to Dependent sum and productCartesian0.60section
Cartesian closed categoryrelated to Dependent sum and productThen0.60section
Cartesian closed categoryrelated to Dependent sum and productC/Z0.60section
Cartesian closed categoryrelated to Dependent sum and productFor0.60section

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