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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 891239, 11 pages
doi:10.1155/2012/891239
Reflective Full Subcategories of the Category of -Posets
College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
Received 3 June 2012; Accepted 31 October 2012
Academic Editor: Josef Diblík
Copyright © 2012 Hongping Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.