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cs.FL2024
Topoi of automata I: Four topoi of automata and regular languages
Ryuya Hora
Both topos theory and automata theory are known for their multi-faceted nature and relationship with topology, algebra, logic, and category theory. This paper aims to clarify the t…
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…