Generalizes categorical theories to coherent theories and proves a duality identifying the 2-category of categorical pretopoi with profinite monoids, further realizing the latter as a full sub-2-category of topoi via classifying topos.
arXiv preprint arXiv:1906.08737 , year=
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Characterizes geometric theories with De Morgan classifying toposes via the amalgamation property of models and gives constructions to produce De Morgan toposes from arbitrary ones.
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Duality theory for categorical theories
Generalizes categorical theories to coherent theories and proves a duality identifying the 2-category of categorical pretopoi with profinite monoids, further realizing the latter as a full sub-2-category of topoi via classifying topos.
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De Morgan's law in toposes I
Characterizes geometric theories with De Morgan classifying toposes via the amalgamation property of models and gives constructions to produce De Morgan toposes from arbitrary ones.