CATEGORICAL ASPECTS OF POWER ALGEBRAS

Abstract

The well-known power algebra construction is investigated from a categorical point of view. We establish basic categorical properties, from which we deduce the Homomorphism and Isomorphism Theorems for power algebras. We show that the power algebra construction induces a monad, called the power algebra monad, and determine the associated Eilenberg-Moore category as well as the associated Kleisli category.