Dear categorists, I have come across a condition on maps between sheaves which I am unable to recognize as with my feeble knowledge of sheaf theory. I would appreciate any hints as to what this condition is about. Succinctly but imprecisely my condition can be expressed as: the inverse image of a sufficiently small section is again a section. More precisely, let p : E -> B be p' : E' -> B be two etale maps over a base space B and let f : E -> E' be a continuous map such that p = f p'. The mystery condition on f is as follows: for every x in B there is a neighborhood U of x, such that for every section s : U -> E' of p' there exists a unique section t : U -> E of p for which t(U) = f^(-1)(s(U)). It follows from this condition that f is mono as a morphism in Sh(B) because such an f is injective on each fiber. But I think the condition says more than that. Am I looking at a standard notion? With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]