2010/06/26 by Alessandra Palmigiano, Palmigiano, Alessandra, Riccardo Re +1
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.GN #math.QA #math.RA
paper · pdf · doi:10.48550/arxiv.1006.5128
arxiv created 2010/06/26 · arxiv updated 2010/06/29
It is well known that if G is an étale topological groupoid then its topology can be recovered as the sup-lattice generated by G-sets, i.e. by the images of local bisections. This topology has a natural structure of unital involutive quantale. We present the analogous construction for any non étale groupoid with sober unit space G0. We associate a canonical unital involutive quantale with any inverse semigroup of G-sets which is also a sheaf over G0. We introduce axiomatically the class of quantales so obtained, and revert the construction mentioned above by proving a representability theorem for this class of quantales, under a natural spatiality condition.