Subtopos
= Subtopos
= Subtoposes
{synonym}
A <subtopos> is a <Grothendieck topos> embedded by a <geometric embedding>, considered up to equivalence over the ambient topos. On a <site> $(\mathcal C,J)$, <subtoposes> correspond to Grothendieck topologies $J'\supseteq J$. On a <classifying topos> this is the <duality between geometric quotients and subtoposes>.