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math.CT2025
Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets
Ryuya Hora, Yuhi Kamio, Yuki Maehara
In the topos of simplicial sets, it makes sense to ask the following question about a given natural number : what is the minimum value such that -skeletality implies -…
math.CT2024
Solution to Lawvere's first problem: a Grothendieck topos that has proper class many quotient topoi
Yuhi Kamio, Ryuya Hora
This paper solves the first of the open problems in topos theory posted by William Lawvere, concerning the existence of a Grothendieck topos that has proper class many quotient top…
math.CT2023★ 2 cited
Quotient toposes of discrete dynamical systems
Ryuya Hora, Yuhi Kamio
This paper gives a classification of classes of discrete dynamical systems (a set equipped with an endofunction) closed under finite limits and small colimits. The conclusion is si…