^{}Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic

Abstract

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in \cite{zhang-laan}, we characterize their subalgebras and quotients, and following \cite{solovyov-qa}, we show that the category of $Q$-sup-algebras is isomorphic to a certain subcategory of a category of $Q$-modules.

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