We continue our investigation of distributions on a topos, the symmetr
ic monad, and complete spreads. Our tool is the pure dense/complete sp
read, or comprehensive, factorization of a geometric morphism. We obta
in, among other results, a characterization of the algebras for the sy
mmetric monad that translates into a ''Waelbroeck'' theorem for topose
s. We also investigate the connection between complete spreads and the
fundamental group of a topos. (C) 1998 Elsevier Science B.V. All righ
ts reserved.