Definition 7.47.8 (00Z6)—The Stacks project

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Definition 7.47.8. Let $\mathcal{C}$ be a category. Let $J$ , $J'$ be two topologies on $\mathcal{C}$ . We say that $J$ is finer or stronger than $J'$ if and only if for every object $U$ of $\mathcal{C}$ we have $J'(U) \subset J(U)$ . In this case we also say that $J'$ is coarser or weaker than $J$ .

Comments (2)

Comment #5418 by Laurent Moret-Bailly on July 24, 2020 at 05:19

There should be a definiton of "coarser" which is used in the following paragraph. Same for the synonyms "stronger" and "weaker" which occur occasionally.

Comment #5645 by Johan on November 14, 2020 at 16:20

Thanks and fixed here.

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