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For questions about sheaves on a topological space.
2
votes
What information is lost in $X \to \mathrm{Sh}(X)$?
Benjamin Steinberg's answer covers the case of topological spaces, so I'll answer this question for sites.
The functor
$$\mathrm{Sh}:\mathbf{Site}\rightarrow\mathbf{Topos}^{\mathrm{op}}$$
(here $\mat …