exponential object

== English == === Noun === 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. ==== Hypernyms ==== internal Hom ==== See also ==== currying ∼ {\displaystyle \sim } exportation_(logic) (an instance of which is the transpositioning λ {\displaystyle \lambda } in the figure) modus ponens (homologous to the universal evaluation morphism, eval {\displaystyle {\text{eval}}} )