On Completions of Posets with Operators

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING（2022）

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摘要

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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关键词

poset with an operator, order-embedding, lax morphism, completion, sup-algebra, injective object, injective hull

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