I would like to know whether somebody knows of an abstract characterization of those geometric morphisms (between elementary toposes) which are of the form Pi_I : E/I -> E for some I in E ? My - maybe misleading - intuition is that a topos is a generalized locale and the functor I* : E -> E/I corresponds to the locale morphisms corresponding to open subspace inclusions. (If L is a locale and x is in L then the mapping y |-> x inf y from L to { z : L | z less or equal x } is the locale morphism corresponding to the open subspace inclusion of the open subset given by x into the space given by L). Maybe it is also wrong to think of a topos simply as generalized locale and that the "generalized locale" is given by the fibration Sub(E) -> E and not by the fibration cod : Map(E) -> E . What I know about open geometric morphisms seems to confirm this latter viewpoint. So I am a bit confused and would appreciate any hints ! Thomas Streicher