Geodesic
Internal parameterization of hyperconnected quotients
Theory and applications of categories, Hofstra Festschrift, Tome 42 (2024), pp. 263-313

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One of the most fundamental facts in topos theory is the internal parameterization of subtoposes: the bijective correspondence between subtoposes and Lawvere-Tierney topologies. In this paper, we introduce a new but elementary concept, "a local state classifier", and give an analogous internal parameterization of hyperconnected quotients (i.e., hyperconnected geometric morphisms from a topos). As a corollary, we obtain a solution to the Boolean case of the first problem of Lawvere's open problems.

Publié le :
Classification : 18B25
Keywords: Topos, hyperconnected geometric morphism, internal semilattice 
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     author = {Ryuya Hora},
     title = {Internal parameterization of hyperconnected quotients},
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Ryuya Hora. Internal parameterization of hyperconnected quotients. Theory and applications of categories, Hofstra Festschrift, Tome 42 (2024), pp. 263-313. http://geodesic.mathdoc.fr/item/TAC_2024_42_a10/