The coherent topology on a small coherent category is generated by finite families of arrows whose image subobjects have union equal to the whole target. Pullback stability of images and unions and closure under composition make these a coverage. On a coherent syntactic category, this is the site topology used to construct the classifying topos of its coherent theory.
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Coherent topology is a type of topology that is often used in the context of sheaf theory and algebraic geometry, particularly to study the behavior of sheaves over topological spaces. It is commonly associated with coherent sheaves, which are a particular type of sheaf that can be thought of as a generalization of vector bundles or modules over a ring.