A **Grothendieck topology** *J* on a category *C* is a collection, *for each object c of C*, of distinguished sieves on *c*, denoted by *J*(*c*) and called **covering sieves** of *c*. This selection will be subject to certain axioms, stated below. Continuing the previous example, a sieve *S* on an open set *U* in *O*(*X*) will be a covering sieve if and only if the union of all the open sets *V* for which *S*(*V*) is nonempty equals *U*; in other words, if and only if *S* gives us a collection of open sets which cover *U* in the classical sense.

Read more about Grothendieck Topology: Sites and Sheaves, Continuous and Cocontinuous Functors

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... In fact Alexander

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