exponential object
English
[edit]![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/ExponentialObject-01.svg/325px-ExponentialObject-01.svg.png)
Noun
[edit]exponential object (plural exponential objects)
- (category theory) An object which indexes a family of arrows between two given objects in a universal way, meaning that any other indexed family of arrows between the same given pair of objects must factor uniquely through this universally-indexed family of arrows.
- An exponential object generalizes its interpretation in category ; namely, that of as a function set or internal hom-set.
- The pair is the terminal object of the comma category . Therefore the exponential object is a kind of universal morphism.
Hypernyms
[edit]See also
[edit]- currying exportation_(logic) (an instance of which is the transpositioning in the figure)
- modus ponens (homologous to the universal evaluation morphism, )