Solovyov, Sergey A. On the category \(Q\)-Mod. (English) Zbl 1145.06008 Algebra Univers. 58, No. 1, 35-58 (2008). 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. Cited in 1 ReviewCited in 24 Documents MSC: 06F07 Quantales 06B23 Complete lattices, completions 06F25 Ordered rings, algebras, modules 18B99 Special categories 54A40 Fuzzy topology Keywords:complete lattice; quantale module; monadic category; tensor product PDFBibTeX XMLCite \textit{S. A. Solovyov}, Algebra Univers. 58, No. 1, 35--58 (2008; Zbl 1145.06008) Full Text: DOI