exponential object
Noun
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.
- Related words
- currying ∼ exportation_(logic)modus ponens
- Broader terms
- internal Hom
- Examples
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An exponential object generalizes its interpretation in category #92;mathbf#123;Set#125;; namely, that of as a function set or internal hom-set.
More examples (1)
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.
Word forms
exponential objects