### A shrinking of a category of societies is a universal partly ordered class

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The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.

The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.