The Stacks project

Remark 7.48.3. Enlarging the class of coverings. Clearly, if $\text{Cov}(\mathcal{C})$ defines the structure of a site on $\mathcal{C}$ then we may add to $\mathcal{C}$ any set of families of morphisms with fixed target tautologically equivalent (see Definition 7.8.2) to elements of $\text{Cov}(\mathcal{C})$ without changing the topology.

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