What does exponential object mean?

exponential object

Word Rarity Rare

Frequency: Zipf frequency 3.31 in modern English

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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."
"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."

exponential objects (plural)

currying ∼ exportation_(logic) modus ponens

currying ∼ exportation_(logic) modus ponens

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