Abstract
This work is third in a tetralogy which develops a universal Existence Theorem for orbifolds. In a preceding paper, the problem was reduced to existence of very technical, very formal categorical topologies dubbed orbifold structures. This paper tackles the problem of generating such subtle topologies.The easiest topologies to generate come from geometric models, in which formal subsets are monomorphic. Our main theorem shows how to create a technical, non-geometric topology from a geometric beginning. In particular, our process generalizes the relationship between the Zariski and étale topologies, from algebraic geometry.