Fundamentals of Quantales

The first section gives a detailed study of the category of complete lattices and join preserving maps. A special focus is put on quotient constructions and the tensor product being part of a natural monoidal structure. On this basis Chap. 2 gives a survey on the theory of quantales as semigroups in the category of complete lattices and join preserving maps. Besides general properties a special attention is devoted to some important subclasses of quantales: Balanced quantales, semi-unital quantales, idempotent quantales, bisymmetric quantales, Frobenius quantales and complete MV-algebras.