Algebraic representation of L-valued continuous lattices via the open filter monad

TL;DR

This paper establishes a connection between $L$-valued continuous lattices and open filter monads using algebraic and topological methods, providing a new categorical perspective on $L$-valued topology.

Contribution

It introduces an algebraic representation of $L$-valued continuous lattices through the open filter monad framework, linking topology and lattice theory.

Findings

Open filters form a monad in $L$-valued topological spaces

Algebras of the open filter monad are exactly $L$-continuous lattices

Uses $L$-Scott topology and specialization $L$-order for characterization

Abstract

With a complete Heyting algebra $L$ as the truth value table, we prove that the collections of open filters of stratified $L$-valued topological spaces form a monad. By means of $L$-Scott topology and the specialization $L$-order, we get that the algebras of open filter monad are precisely $L$-continuous lattices.