= Morita equivalence of geometric theories
{c}
{title2=$\mathbf{Set}[\mathbb T]\simeq\mathbf{Set}[\mathbb S]$}
<Geometric theories> are Morita-equivalent when their <classifying toposes> are equivalent. This gives equivalent internal model categories pseudonaturally in every <Grothendieck topos>. A common <classifying topos> transports intrinsic invariants between different presentations; agreement of set-valued model categories alone is insufficient. The <duality between geometric quotients and subtoposes> transfers <geometric theory> extensions along such an equivalence.
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