Date: Tue, 26 Jul 1994 09:04:50 +0500 (GMT+4:00) From: categories Subject: characterization of geometric morphisms of the form Pi_I ?? Date: Wed, 20 Jul 94 20:32:52 +0200 From: Thomas Streicher 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 Date: Thu, 27 Oct 1994 18:27:33 +0500 (GMT+4:00) From: categories Subject: are local homemorphism part of a factorization system Date: Thu, 27 Oct 94 16:27:20 +0100 From: Thomas Streicher Does anyone know whether in the category Geom of toposes and geometric morphism the local homemorphisms form the mono part of a factorization system ? Or is that at least the case in the luff subcategory where one has only essential geomtric morphism whose leftmost adjoint preserves pullbacks. Has this latter category ever been srudied ? Thomas Streicher