Injective locales over perfect embeddings and algebras of the upper powerlocale monad

Abstract

We show that the locales which are injective over perfect sublocale embeddings coincide with the underlying objects of the algebras of the upper powerlocale monad, and we characterize them as those whose frames of opens enjoy a property analogous to stable supercontinuity.

Keywords

• Injective locale
• Perfect embedding
• Powerlocale
• Free frame
• Kock-Zöberlein monad
• Stably supercontinuous lattice