4 papers · 1 filter
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…
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…
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 -…
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…