# exponential object

## English[edit]

### 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.