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Hayato Nasu (Apr 20 2026 at 00:34):Concrete sites are often used to define concrete sheaves, but what class of toposes do the toposes of (non-concrete) sheaves on (small) concrete sites form? More specifically, how is it different from local toposes?
By the characterization of local sites, we can show that the topos of sheaves on a (small) concrete site is local, as shown in this nLab page. Although the converse does not hold at the level of sites, it does not directly imply that the classes of toposes of sheaves are different.
David Michael Roberts (Apr 20 2026 at 01:15):I think perhaps your second link doesn't go where you meant it to!
Hayato Nasu (Apr 20 2026 at 01:33):Thanks! I hope it's fixed now.