Dear all, If (C,J) is a site, then the category Sh(C) can be presented as a category of fractions Psh(C)[D^-1] where D is the class of J-dense monomorphisms. Morphisms in here are equivalence classes of partial maps X --> Y whose domain is dense in X, and where the equivalence relation is generated by the 2-cells of spans. This is all well known. I am wondering if there is a reference for the following fact: if one restricts to separated presheaves, then every equivalence class of morphisms has a maximal representative, given by the dense partial maps X <--< X' ---> Y whose graph X' >---> X*Y is a J-closed monomorphism. So between separated presheaves, no quotienting is necessary---beyond that inherent in the notion of subobject---though now composition is no longer span composition on equivalence classes, but rather span composition followed by J-closure. The proof is rather easy but I am wondering if there is the even easier possibility of citing something. Thanks! Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]