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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Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.
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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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Smooth categories in a 6 functor formalism and compact generation for nuclear categories in analytic geometry
Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.