Definition from Wiktionary, the free dictionary
- (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.