The Stacks project

Definition 8.10.2. Let $\mathcal{C}$ be a site. Let $p : \mathcal{S} \to \mathcal{C}$ be a fibred category. We say $(\mathcal{S}, \text{Cov}(\mathcal{S}))$ as in Lemma 8.10.1 is the structure of site on $\mathcal{S}$ inherited from $\mathcal{C}$. We sometimes indicate this by saying that $\mathcal{S}$ is endowed with the topology inherited from $\mathcal{C}$.

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View Definition 8.10.2 as pdf