Definition 6.128.
Let \(C\) be a local pretopos. The effective epi topology on \(C\) is defined as follows: a sieve on \(X \in C\) is declared to be a covering sieve if it contains a finite family \((Y_i \to X)_i\) such that the map \(\bigsqcup_i Y_i \to X\) is an effective epimorphism.
If \(C\) is small, we obtain a topos \(\Shv(C)\) with respect to this topology.