An Application of Idempotent Monads and Comonads to Compactifications and Unitizations

This paper uses monads and comonads to establish a certain type of equivalence between two subcategories, one reflective and one coreflective, in a category whose objects represent compactifications of non-compact locally compact Hausdorff spaces. The equivalence is then examined in the dual category of unitizations of non-unital commutative $C^{\ast }$-algebras and subsequently generalized to the noncommutative case.