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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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Morphism on schemes induced by continuous morphism of sites

If $X$ is also locally of finite type, there is a canonical functor $\pi_X:X_{et} \to LFtyp$ sending each etale map $X' \to X$ to $X'.$ This is a morphism of sites which induces the geometric morphism … In particular, any map of sites $f:X_{et} \to Y_{et}$ commuting over their projections to $LFtyp$ encodes a morphism $X \to Y.$ However, this is too strict, since maps of ringed topoi need not respect …
David Carchedi's user avatar