Spreads and the symmetric topos II Original Research Article

We continue our investigation of distributions on a topos, the symmetric monad, and complete spreads. Our tool is the pure dense/complete spread, or comprehensive, factorization of a geometric morphism. We obtain, among other results, a characterization of the algebras for the symmetric monad that translates into a “Waelbroeck” theorem for toposes. We also investigate the connection between complete spreads and the fundamental group of a topos.