Year: 2025
Type: article
Abstract: Based on a complete Heyting algebra $L$, we first propose the concept of $L$-quasi-convex spaces and construct an adjunction between the category of $L$-$S_0$-quasi-convex spaces and the opposite category of complete $L$-ordered sets. Then we present the concept of weakly fuzzy algebraic lattices and prove that an $L$-quasi-convex structure endowed with the fuzzy inclusion order is precisely a weakly fuzzy algebraic lattice. Secondly, we introduce the notion of sobriety in $L$-quasi-convex spaces from the perspective of categorical equivalence, showing that the category of sober $L$-quasi-convex spaces is dually equivalent to that of weakly fuzzy algebraic lattices. Finally, we construct a monad on the category of $L$-$S_0$-quasi-convex spaces and obtain that the Eilenberg–Moore algebras of this monad are precisely sober $L$-quasi-convex spaces.
Authors: Licong Sun, Bin Pang
Institution: Beijing Institute of Technology
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: G4820953449, G5167407451, G6803533185
OpenAlex ID: W7117578403