exponential object

noun

Definitions

  1. An object which indexes a family of arrows between two given objects in a universal way,…

    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.

The neighborhood

Vish — recursive loop

No curated loop yet for exponential object. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA