Effective equivalence relations and principal quantales
arXiv:1807.08979 · doi:10.1007/s00233-019-09994-z
Abstract
Stably supported quantales generalize pseudogroups and provide an algebraic context in which to study the correspondences between inverse semigroups and étale groupoids. Here we study a further generalization where a non-unital version of supported quantale carries the algebraic content of such correspondences to the setting of open groupoids. A notion of principal quantale is introduced which, in the case of groupoid quantales, corresponds precisely to effective equivalence relations.
v2 contains new preliminary material in the introduction