Dictionary
Words, grammatical forms and meanings linked to the ontology.
exponential object en · NOUN
Meanings
-
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.
Forms
Hypernyms
internal Hom
Relateds
currying ∼ exportation_(logic) · modus ponens