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arXiv · 2302.06851

Internal Parameterization of Hyperconnected Quotients

Ryuya Hora
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Abstract

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.

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Ryuya Hora. 2023-02-14. Internal Parameterization of Hyperconnected Quotients. https://doi.org/10.70930/tac%2Fa8ppg8i1

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