exponential object
noun1
Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences 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 #92;mathbf#123;Set#125;; namely, that of as a function set or internal hom-set.
- The pair Z^Y,#92;mbox#123;eval#125;#58;Z^Y#92;timesY#92;rightarrowZ is the terminal object of the comma category (-#92;timesY)#92;downarrowZ. Therefore the exponential object is a kind of universal morphism.
- Related terms
- currying ∼ exportation_(logic), modus ponens
- Hypernyms
- internal Hom