The purpose of this paper is to show how certain interesting structure
s, models of coherent first-order theories on the one hand and Grothen
dieck topologies on the other, may be viewed as split opfibrations. In
the course of doing so, two general classes of split opfibrations wil
l be defined of which models and topologies comprise two special examp
les. (C) 1997 Elsevier Science B.V.