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.
The Equivalence Extension Property and Model Structures
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abstract
We give an elementary construction of a certain class of model structures. In particular, we rederive the Kan model structure on simplicial sets without the use of topological spaces, minimal complexes, or any concrete model of fibrant replacement such as Kan's Ex^infinity functor. Our argument makes crucial use of the glueing construction developed by Cohen et al. in the specific setting of certain cubical sets.
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math.CT 1years
2026 1verdicts
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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.