In the context of category theory, an **exponential object** is a way to generalize the concept of a function space to arbitrary categories. ### Definition Given a category \(\mathcal{C}\), for objects \(A\) and \(B\) in \(\mathcal{C}\), an exponential object \(B^A\) is an object that represents the space of morphisms from \(A\) to \(B\).
Articles by others on the same topic
An exponential object represents maps out of a product with : there are natural bijectionsThe corresponding operations are currying and uncurrying, and the identity of corresponds to the evaluation morphism .