Injective Hulls of Quantale-Enriched Multicategories

TL;DR

This paper extends the theory of quantale-enriched multicategories by proving the existence of injective hulls for such structures and explores their relation to classical topological constructs.

Contribution

It generalizes Rump's results to quantale-enriched multicategories and establishes a link between injective hulls and the Isbell adjunction in topology.

Findings

Every quantale-enriched multicategory admits an injective hull.

Connections are drawn between injective hulls and the Isbell adjunction.

Generalization of classical results to enriched categorical contexts.

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.