An extensive discussion of sites and logical operations on related categories can be found in the article [74] by Gonzalo Reyes. ### Elementary sites A topology on an elementary topos $ mathcal{E} $ is by definition any arrow $ j:OmegatoOmega $ that satisfies 1. $ jcircmathit{true}=mathit{true} $ 2. $ jcirc j=j $ 3. $ curvearrowrightcirc(jtimes j)=jcirccurvearrowright $ . The pair $ mathcal{E}_{j}=(mathcal{E}