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math.CT2025
Normalization of a subgroup, in a topos, and of a word-congruence
Ryuya Hora
This paper provides a new categorical definition of a normalization operator motivated by topos theory and its applications to algebraic language theory. We first define a normaliz…
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.CT2025
Grothendieck topoi with a left adjoint to a left adjoint to a left adjoint to the global sections functor
Ryuya Hora
This paper introduces the notion of complete connectedness of a Grothendieck topos, defined as the existence of a left adjoint to a left adjoint to a left adjoint to the global sec…