**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.

Read more about Cartesian Closed Category: Definition, Examples, Applications, Equational Theory

### Other articles related to "cartesian closed category, cartesian closed, closed":

**Cartesian Closed Category**- Equational Theory

... In every

**cartesian closed category**(using exponential notation), (XY)Z and (XZ)Y are isomorphic for all objects X, Y and Z ... One may ask what other such equations are valid in all

**cartesian closed**categories ... the terminal object of C) 1x = 1 x1 = x (x×y)z = xz×yz (xy)z = x(y×z) Bicartesian

**closed**categories extend

**cartesian closed**categories with binary coproducts and an initial object ...

... various Alcan facilities on the 53-acre site

**closed**between 2006 and 2007 ... The laboratory was also

**closed**in 2004 and demolished in 2009 ... The former Hunt Edmunds brewery premises became Crest Hotels headquarters, but

**closed**in the late 1970s and was abandoned in the late 1980s, while ...

... Yering is a

**closed**railway station, located up from Macintyre Lane, Yering, Victoria, Australia, on the now-

**closed**Healesville greater-metropolitan line ... The station was

**closed**in 1980, however the line was not officially

**closed**until 10 March 1983 ...

**Closed**station navigation Healesville line ← Previous station Coldstream

1856 London, Istanbul-Galata, Symirna, Galaţi (

**closed**in 1866), Beyrouth (

**closed**in 1921) 1861 Bucarest (

**closed**in 1866) 1862 Salonika, Aydin, Afyon Carahissar (

**closed**. 1906 Xanthi (

**closed**in 1914), Erzurum, Giresun, Kutahya, Gaziantep, Silifke (

**closed**in 1907), Famagusta, Haifa, Tripoli (Libya) (

**closed**in 1912) 1907 Adapazari, Mosul, Minieh 1908 Tarsus, Homs (

**closed**in 1921. 1912 Bolu, Urfa, Sandıklı, Söke, Djeddah (

**closed**in 1916) 1913 Iskenderun (

**closed**in 1921) 1914 Canakkale, Zahleh (

**closed**in 1921) 1916 Marseille 1918 ...

### Famous quotes containing the words category and/or closed:

“Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the *category* of such classes.”

—Vladimir Ilyich Lenin (1870–1924)

“What I call middle-class society is any society that becomes rigidified in predetermined forms, forbidding all evolution, all gains, all progress, all discovery. I call middle-class a *closed* society in which life has no taste, in which the air is tainted, in which ideas and men are corrupt. And I think that a man who takes a stand against this death is in a sense a revolutionary.”

—Frantz Fanon (1925–1961)