exponential object
（ plural ）
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(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.
exponential object
In many cartesian closed categories, the exponential object BA serves as a universal classifier for morphisms from A to B, so any family of arrows from A to B indexed by an object X factors uniquely through the exponential object.
In many cartesian closed categories, the exponential object BA serves as a universal classifier for morphisms from A to B, so any family of arrows from A to B indexed by an object X factors uniquely through the exponential object.
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