= Duality between geometric quotients and subtoposes
{title2=$\{\mathbb T'\text{ geometric quotient of }\mathbb T\}\leftrightarrow\operatorname{Subtop}(\mathbf{Set}[\mathbb T])$}
Each <geometric quotient theory> is classified by the corresponding <subtopos> of the original <classifying topos>. Extra axioms impose extra covers on the <geometric syntactic topology>. Conversely additional definable covers give the corresponding deductively closed quotient. Under <Morita equivalence of geometric theories>, transporting a <subtopos> produces a corresponding quotient of the other theory, with equivalent classifiers. Stronger axioms correspond to smaller <subtoposes> under inclusion.
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