Algebraic representation of finite-complete $L$-ordered sets by monad

Abstract

Choosing quantales as lattice-valued environment, we introduce a monad $\mathbb{S}$ by finite $L$-subsets and then construct the corresponding adjoint functors. Moreover, we prove that the monad $\mathbb{S}$ is a submonad of $L$-semifilter monad. Finally, we investigate $L$-closure operators and finite-complete $L$-ordered sets by $\mathbb{S}$.

Keywords

• adjoint functor
• Eilenberg-Moore category
• Kleisli category
• L-ordered set

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