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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.CO2024
The bounds of rigid sphere design
Yuhi Kamio
We have identified some necessary conditions for the existence of rigid sphere designs. In particular, we have successfully resolved the conjecture proposed by [Ban87]; Given fixed…