Abstract
Abstract A synthesis of notions arising from algebraic geometry, especially those developed by Verdier in Seminaire de Geometric Algebrique IV, and the notion of topological functor (in the sense of G.C.L. Brummer and R.-E. Hoffmann) is made. In particular, Grothendieck topologies are shown to be topological over the category of categories with pullbacks and pullback preserving functors, and consequences derived.
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