Writings

Solution to Lawvere's first problem: A Grothendieck topos that has proper class many quotient topoi

Journal Yuhi Kamio, Ryuya Hora Advances in Mathematics 487, 110751 March 2026

Gives a solution to Lawvere's first open problem.

• Topos
• Combinatorics
• Logic

• DOI
• arXiv

See also: Lawvere's open problems

Talks: Ph.D. thesis presentation (2026) · UTokyo Logic seminar (2025)

Grothendieck topoi with a left adjoint to a left adjoint to a left adjoint to the global sections functor

Journal Proceedings of the American Mathematical Society 154(2), 567-584 February 2026

Studies completely connected topoi and gives a site characterization with examples.

• Topos
• Category
• Combinatorics

• DOI
• arXiv

Talks: Ph.D. thesis presentation (2026) · UTokyo Logic seminar (2025)

Normalization of a subgroup, in a topos, and of a word-congruence

arXiv preprint arXiv:2511.05012 7 November 2025

Defines a generalized normalization operator motivated by topos theory and algebraic language theory.

• Topos
• Automaton
• Algebra
• Combinatorics

• arXiv

Games as recursive coalgebras: A categorical view on the Nim-sum

arXiv preprint arXiv:2510.22886 27 October 2025

Reinterprets impartial combinatorial games and the Nim-sum using recursive coalgebras.

• Game
• Coalgebra
• Category
• Algebra

• arXiv

Talks: CSCAT 2024 (2024) · 7th Japan Combinatorial Game Theory Conference (2023) · Japan Combinatorial Game Theory Mini-Workshops with Urban Larsson (2023)

Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets

arXiv preprint Ryuya Hora, Yuhi Kamio, Yuki Maehara arXiv:2503.03439 5 March 2025

Gives a preprint solution to one of Lawvere's seven open problems through levels in the topos of symmetric simplicial sets.

• Topos
• Combinatorics

• arXiv

Talks: Ph.D. thesis presentation (2026) · UTokyo Logic seminar (2025)

Topoi of automata I: Four topoi of automata and regular languages

arXiv preprint arXiv:2411.06358 10 November 2024

Introduces a topos-theoretic point of view on formal language theory.

• Automaton
• Topos
• Geometry

• arXiv

Talks: SLACS 2025 (2025) · CT 2025 (2025) · Theoretical Cosynus Seminar (2025) · Séminaires du LIPN (2025) · IRIF Sémantique seminar (2025) · Groupe de travail topossique (2025) · Categories for Automata and Language Theory (2025) · Groupe de travail topossique (2025) · CSCAT 2025 (2025) · CMUP SAL seminar (2025) · Young Automata Theorists Gathering in Japan (2024)

Internal parameterization of hyperconnected quotients

Journal Theory and Applications of Categories 42(11), 263-313 23 August 2024

Introduces local state classifiers and uses them to establish an internal parameterization of hyperconnected quotients.

• Topos
• Category

• DOI
• TAC
• arXiv

See also: Lawvere's open problems

Talks: Theoretical Cosynus Seminar (2025) · Séminaires du LIPN (2025) · IRIF Sémantique seminar (2025) · Groupe de travail topossique (2025) · Toposes in Mondovì (2024) · Category Theory 2023 (2023) · Australian Category Seminar (2023) · CSCAT 2023 (2023)

Quotient toposes of discrete dynamical systems

Journal Ryuya Hora, Yuhi Kamio Journal of Pure and Applied Algebra 228(8), 107657 August 2024

Classifies classes of discrete dynamical systems closed under finite limits and small colimits.

• Topos
• Dynamics
• Algebra
• Combinatorics

• DOI
• arXiv

See also: Lawvere's open problems

Talks: CT 2024 (2024)