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

With a frame L as the truth value table, we prove that the collections of open filters of T-0 L-topological spaces form a monad. By means of L-Scott topology and the specialization L-order, we get the main results: (1) the Eilenberg-Moore algebras of the open filter monad are precisely L-continuous lattices; (2) the category of L-continuous lattices is strictly monadic over the category of T-0 L-topological spaces. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The paper demonstrates that the collections of open filters of T-0 L-topological spaces form a monad, and concludes that the Eilenberg-Moore algebras of the open filter monad are precisely L-continuous lattices. Additionally, it shows that the category of L-continuous lattices is strictly monadic over the category of T-0 L-topological spaces.