It is well known that injective objects play a fundamental role in many branches of mathematics. The question whether a given category has enough injective objects has been investigated for many categories. Also, quasi-injective modules and acts have been studied by many categorists. In this paper, we study quasi-injectivity in the category of actions of an ordered monoid on ordered sets (Pos-S) with respect to embeddings. Also, we give the relation between injectivity, quasi-injectivity (with respect to embeddings), and poset completeness in the category Pos-S and some of its important subcategories.
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