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On the category \(Q\)-Mod. (English) Zbl 1145.06008

Summary: In this paper we consider the category \(Q\)-Mod of modules over a given quantale \(Q\). The paper is motivated by constructions and results from the category of modules over a ring. We show that the category \(Q\)-Mod is monadic, consider its relation to the category \(Q\)-Top of \(Q\)-topological spaces and generalize a method of completion of partially ordered sets.

MSC:

06F07 Quantales
06B23 Complete lattices, completions
06F25 Ordered rings, algebras, modules
18B99 Special categories
54A40 Fuzzy topology
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