On Completions of Posets with Operators

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Authors

ZHANG Xia PASEKA Jan MA Wen

Year of publication 2022
Type Article in Periodical
Magazine / Source Journal of Multiple-Valued Logic and Soft Computing
MU Faculty or unit

Faculty of Science

Citation
Web https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-38-number-1-2-2022/mvlsc-38-1-2-p-227-243/
Keywords poset with an operator; order-embedding; lax morphism; completion; sup-algebra; injective object; injective hull
Description In this note, we study completions of posets with a closure operation. Firstly, we show that every such completion is injective in the category of posets with a closure operation with respect to a subclass of order embeddings. Moreover, we show how to construct injective hulls for arbitrary posets with a closure operation.
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