Reflective Full Subcategories of the Category of L-Posets

Abstract EN

This paper focuses on the relationship between L-posets and complete L-lattices from the categorical view.

By considering a special class of fuzzy closure operators, we prove that the category of complete L-lattices is a reflective full subcategory of the category of L-posets with appropriate morphisms.

Moreover, we characterize the Dedekind-MacNeille completions of L-posets and provide an equivalent description for them.