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Distributive idempotents in an order-enriched category
Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 278-300.

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We introduce distributive maps between lattices and consider the categorical assumption that distributive idempotents split. We explore this assumption in the context of a categorical axiomatization of the category of locales. The assumption is shown to be stable under groupoids (this includes slice stability) and we further show that it implies that triquotient surjections are effective descent morphisms. This result follows even without assuming that the underlying (axiomatized) category of locales has coequalizers.
Publié le :
Classification : 06D22, 03G30
Keywords: Locale, topos, categorical logic, powerlocales, order enriched, distributive lattice, axioms 
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     author = {Christopher Townsend},
     title = {Distributive idempotents in an order-enriched category},
     journal = {Theory and applications of categories},
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     volume = {40},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_40_a8/}
}
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Christopher Townsend. Distributive idempotents in an order-enriched category. Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 278-300. http://geodesic.mathdoc.fr/item/TAC_2024_40_a8/