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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 891239, 11 pages
http://dx.doi.org/10.1155/2012/891239
Research Article

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.