Injective Hulls of Quantale-Enriched Multicategories

Abstract

In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, we show that every quantale-enriched multicategory admits an injective hull. Finally, we expose a connection between the Isbell adjunction and the construction of injective hulls for topological spaces made by Banaschewski in 1973.