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.

“An exponential object generalizes its interpretation in category #92;mathbf#123;Set#125;; namely, that of as a function set or internal hom-set.”

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Meanings

nounexponential object (plural exponential objects)

plural exponential objects

  1. category theoryAn 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.

    1 more example

    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.

Cite this entry
APA

exponential object. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/exponential%20object

MLA

“exponential object.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/exponential%20object. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “exponential object,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/exponential%20object.

Source: exponential object on Wiktionary, CC BY-SA 4.0.