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For questions related to the mathematical notion of site, which among others generalizes the notion of topological space. For questions on internet-sites, use online-resources, but note that these questions need to be very specific to research-level mathematics to be on-topic.

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Why is $1$ not a dense sub-site in a group with the trivial Grothendieck topology?

Yes, your counterexample seems to be correct — there’s an error in Def C2.2.1 as printed. This issue is mentioned in the n-lab’s article on dense sub-site (current revision permalink), which notes a …
Peter LeFanu Lumsdaine's user avatar