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Paper IPM / M / 16478  


Abstract:  
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, quasiinjective modules and acts have been
studied by many categorists. In this paper, we study quasiinjectivity in the category of actions of an ordered monoid on ordered sets (PosS) with respect to embeddings. Also,
we give the relation between injectivity, quasiinjectivity (with respect to embeddings), and poset completeness in the category PosS and some of its important subcategories.
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