Geodesic
On monadic quantale algebras: basic properties and representation theorems
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 91-118

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Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
Keywords: m-semilattice, ⋁-lattice, quantale, quantale module, topological system, tropological system, quantale algebra, quantaloid, quantale algebroid, quantifier, monadic quantale algebra, Girard quantale, Q-equivalence relation, Ω-valued set, GL-monoid, commutative integral cl-monoid 
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Solovyov, Sergey. On monadic quantale algebras: basic properties and representation theorems. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 91-118. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a4/