Generalized logic and the representation of rings
Various authors considered weaker and weaker logics and, in particular, studied ``quantale-valued sets'' (equivalently, ``sheaves over a quantale''). The authors introduce ``quantic sheaves'' using some ideas from enriched category theory to motivate a quantic sheaf. If a localic subquantale of \(Q\) is given, it turns out that a quantic sheaf over \(Q\) gives a sheaf in the usual sense. As an application, the authors derive some sheaf representations for commutative rings including the Pierce representation.
sheaf representations for commutative rings
scientific article; zbMATH DE number 934060