(People use also expressions: quantale module, quantic module)

Idea

A quantale is an analogue of a noncommutative ring and a noncommutative generalization of a locale; it is a semigroup in the monoidal category of sup-lattices; therefore, for a quantale $Q$, a left $Q$-module should be a sup-lattice $M$ together with an action $Q\otimes M\to M$ satisfying the usual axioms. In the special case when the quantale is unital and commutative and hence a locale, such a module is called a “localic module”, or module over a locale. The multiobject generalization is called a quantaloid module.

References

Isar Stubbe, Q-modules are Q-suplattices, Theory and Appl. of Cat. 19, 2007, No. 4, pp 50-60 abs