Let E be the category of presheaves on space X and S the category of sheaves on the same space, clearly the category of separated presheaves on X, call it P, is between E and F. ?In more detail, P is the full subcategory of E determined by the separated presheaves on X.? I suppose that P is not a topos in general, but I am wondering if anyone knows of a nice characterization of it, or indeed whether there are any papers on this topic. Neither Barr and Wells' TTT nor Peter Johnstone's book says enough about separated presheaves for my current explorations of the connections between sheaf-theoretic ideas and some questions in software systems theory that I am working on with Rakesh Dubey. Any suggestions will be most appreciated. Thanks, David