Ryuya Hora 洞龍弥

Research interests

• Topos theory: Quotient topoi; Applications to computer science and formal language theory
• Coalgebras: Automata; Discrete dynamical systems; Combinatorial games
• Category theory: Categorical logic; Categorical algebra

Education

• April 2024 – March 2026 Ph.D. in Mathematics, Graduate School of Mathematical Sciences, The University of Tokyo
  Thesis: Connectedness and full subcategories of topoi (advisor: Ryu Hasegawa)
• April 2022 – March 2024 Master of Mathematics, Graduate School of Mathematical Sciences, The University of Tokyo
  Thesis: Two classification theorems of quotient toposes (advisor: Ryu Hasegawa)
• April 2020 – March 2022 Bachelor of Science, Department of Mathematics, Faculty of Science, The University of Tokyo
  Graduated first in the Mathematics Department.
• April 2018 – March 2020 College of Arts and Sciences, Junior Division, The University of Tokyo
• April 2015 – March 2018 Tokuyama High School (山口県立徳山高等学校)

Positions

• April 2026 – presentAssistant Professor, ZEN University
• April 2026 – presentResearcher, Humai Center, ZEN University
• April 2025 – March 2026Research Associate, Centre for Topos Theory and its Applications (CTTA)
  Visit to Paris: 10 April 2025 – 27 June 2025
• July 2022 – March 2025Research Assistant, AFSA project / NII Kanda Lab

Grants and fellowships

• 31 July 2026 – 31 March 2028 (scheduled)Grant-in-Aid for Research Activity Start-up (KAKENHI 26K24500)
• April 2024 – March 2026JSPS Research Fellow (DC1), Japan Society for the Promotion of Science
• 23 April 2024 – 31 July 2026Research grant for JSPS Fellows (KAKENHI 24KJ0837)
• April 2022 – March 2026FoPM course student, The Forefront Physics and Mathematics Program to Drive Transformation
  Financial support: October 2022 – March 2024
• April 2025 – March 2026National Institute of Informatics 2025 Open Collaborative Research Program (251M-22791), Co-Investigator: 組合せゲーム理論の応用可能性の探求 (Exploration of the Applicability of Combinatorial Game Theory)

Awards

• March 2026Dean's award and Graduation Representative, Graduate School of Mathematical Sciences, The University of Tokyo, doctoral course.
• October 2025SLACS 2025 presentation award.
• 21 March 2024Dean's award and Graduation Representative, Graduate School of Mathematical Sciences, The University of Tokyo, master's course.
• 25 March 2022Faculty of Science encouragement award, The University of Tokyo.

Papers

1. Yuhi Kamio, Ryuya Hora. Solution to Lawvere's first problem: A Grothendieck topos that has proper class many quotient topoi. Advances in Mathematics 487, 110751, 2026. DOI · arXiv
2. Ryuya Hora. Grothendieck topoi with a left adjoint to a left adjoint to a left adjoint to the global sections functor. Proceedings of the American Mathematical Society 154(2), 567-584, 2026. DOI · arXiv
3. Ryuya Hora. Normalization of a subgroup, in a topos, and of a word-congruence. arXiv:2511.05012 (preprint), 2025. arXiv · PDF
4. Ryuya Hora. Games as recursive coalgebras: A categorical view on the Nim-sum. arXiv:2510.22886 (preprint), 2025. arXiv
5. Ryuya Hora, Yuhi Kamio, Yuki Maehara. Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets. arXiv:2503.03439 (preprint), 2025. arXiv
6. Ryuya Hora. Topoi of automata I: Four topoi of automata and regular languages. arXiv:2411.06358 (preprint), 2024. arXiv
7. Ryuya Hora. Internal parameterization of hyperconnected quotients. Theory and Applications of Categories 42(11), 263-313, 2024. DOI · TAC · arXiv
8. Ryuya Hora, Yuhi Kamio. Quotient toposes of discrete dynamical systems. Journal of Pure and Applied Algebra 228(8), 107657, 2024. DOI · arXiv

In preparation

• Topoi of automata II: Hyperconnected geometric morphisms and syntactic topoi — draft
• Subtopoi of free monoid actions (with Morgan Rogers)
• Demystifying local state classifiers: local state classifier in a total category with a factorization system (with Yuto Ikeda)
• Notes on Rieg theory: semiring with exponentials in logic, profinite arithmetic, enumerative combinatorics, and category theory — draft
• Differential calculus of impartial combinatorial games (with Ryo Suzuki)
• Topoi with enough projectives
• Topoi of automata III: Geometry of \(\Sigma\)-sets
• Dynamical systems on pretopological spaces — draft
• An enriched-categorical origin of \(\varepsilon\)-transition
• Category Theoretic Ordinal Invariants
• Totally disconnected topoi
• A topos-theoretic view on Gabriel's theorem — draft
• The lattice of hyperconnected quotients is a module of the semiring of productive weak topologies
• When do finite presheaves form a topos? (with Jérémie Marquès)
• Local state classifier, permutation model, and the internal axiom of choice
• A note on language measurability — draft
• Twisted Regular Tetrahedra and Eisenstein Integers

Expository

• 順序集合で遊ぶKan拡張入門, November 2021 · PDF
• 圏論のToy Exampleとしての集合演算, May 2021 · PDF
• 圏論に登場する矢印の意味は—特集 圏論の質問箱. 数学セミナー 2025年11月号, November 2025 · 日本評論社 · CiNii Research
• 安福智明, 洞龍弥, 稲津大貴, 木谷裕紀, 末續鴻輝, 吉渡叶. 準完全情報ニム. 情報処理学会研究報告アルゴリズム（AL）, January 2026 · researchmap · IPSJ

Talks and presentations

2026

1. Title pending. ItaCa Fest 2026, online, 29 September 2026. planned.
2. 文字列から現代数学へ. 数学カフェ 先端講演, Tokyo, Japan, 12 September 2026. planned. Outreach.
3. 圏論は役に立つのか：数学者とエンジニアの対話から考える夜 (Ryuya Hora, Kory). 圏論NIGHT, Tokyo, Japan, 5 September 2026. Outreach.
4. AIについて数学者は(何を)考えるべきか. AI for Math勉強会 第2回, Tokyo, Japan, 17 July 2026. Outreach.
5. ベン図からトポスへ. Math Space Topos 2026 new welcome event, 23 May 2026. Outreach.
6. A Rota-Baxter equation for winning games. Differentiation in category theory and program semantics, Kyoto, Japan, 6 April 2026.
7. A space⋊time for Conway’s Game of Life. CSCAT 2026, Fukui, Japan, 16 March 2026.
8. Measure-theoretic closure operators on formal languages (Ryuya Hora, Ryoma Sin'ya). PPL 2026, Takamatsu, Japan, 11 March 2026. Poster.
9. Turning lights out with the Snake Lemma (Kyosuke Higashida). 20th CGP project, Chofu, Japan, 22 February 2026.
10. Connectedness and full subcategories of topoi. Ph.D. thesis presentation, Tokyo, Japan, 23 January 2026.

2025

1. Local state classifier, The axiom of choice, and permutation model. UTokyo Logic seminar, Tokyo, Japan, 5 December 2025.
2. Connectedness and full subcategories of topoi. UTokyo Logic seminar, Tokyo, Japan, 28 November 2025.
3. Topoi of automata. SLACS 2025, Akita, Japan, 31 October 2025.
4. Topoi of automata. CT 2025, Brno, Czech Republic, 17 July 2025.
5. A topos for regular language theory. Theoretical Cosynus Seminar, Palaiseau, France, 11 June 2025.
6. Local state classifier for automata theory. Séminaires du LIPN, Villetaneuse, France, 5 June 2025.
7. Local state classifier for automata theory. IRIF Sémantique seminar, Paris, France, 27 May 2025.
8. Local state classifier for algebraic language theory. Groupe de travail topossique, Paris, France, 16 May 2025.
9. Topoi of automata. Categories for Automata and Language Theory, Paris, France, 6 May 2025.
10. Topoi of automata. Groupe de travail topossique, Paris, France, 30 April 2025.
11. Topoi of automata. CSCAT 2025, Kumamoto, Japan, 11 March 2025.
12. Topoi of automata. CMUP SAL seminar, online, 28 February 2025.

2024

1. Quotient topoi and geometry of computation. AFSA area meeting, Tokyo, Japan, 30 November 2024. Outreach.
2. The colimit of all monomorphisms classifies hyperconnected geometric morphisms. Toposes in Mondovì, Mondovì, Italy, 10 September 2024.
3. Topos theory as a tool of automata theory. Young Automata Theorists Gathering in Japan, Akita, Japan, 29 August 2024.
4. Quotient toposes of discrete dynamical systems. CT 2024, Santiago de Compostela, Spain, 28 June 2024.
5. アイゼンシュタイン整数と組合せ論. Math Space Topos 2024 new welcome event, 18 May 2024. Outreach.
6. 圏論の利用と濫用. 18th AFSA Colloquium, Tokyo, Japan, 24 April 2024.
7. Introduction to topos theory. 代数トポロジー若手の会, Nagoya, Japan, 16 March 2024.
8. Combinatorial games as recursive coalgebras. CSCAT 2024, Chiba, Japan, 15 March 2024.

2023

1. Constructive mathematics and representation theory. 数学基礎論若手の会2023, Kyonan, Chiba, Japan, 10 December 2023.
2. Category Theory and Combinatorial Game Theory. 7th Japan Combinatorial Game Theory Conference, Tokyo, Japan, 21 August 2023.
3. 母関数の種. Math Space Topos 2023 new welcome event, 15 July 2023. Outreach.
4. Internal parameterization of hyperconnected quotients. Category Theory 2023, Louvain-la-Neuve, Belgium, 6 July 2023.
5. Grundy Numbers and Categories. Japan Combinatorial Game Theory Mini-Workshops with Urban Larsson, Tokyo, Japan, 12 May 2023.
6. Internal parameterization of hyperconnected quotients. Australian Category Seminar, online, 19 April 2023.
7. Internal parameterization of hyperconnected quotients. CSCAT 2023, Kyoto, Japan, 10 March 2023.

2022

1. 順序集合で遊ぶKan拡張. Math Space Topos 2022 new welcome event, 4 June 2022. Outreach.

2021

1. ゼータ関数とメビウス反転. Math Space Topos 2021 new welcome event, 4 December 2021. Outreach.

Teaching, outreach and service

• July 2020 – presentTutor, Math Space Topos
• June 2025 – presentAdvisor, 角川ドワンゴ学園 研究部
• April 2024 – presentFounder and representative, Categories in Tokyo — A series of domestic research conferences in category theory.
• June 2026 – presentFounder and organizer, BiSCiT — A bimonthly seminar series of Categories in Tokyo.
• June 2026 – presentFounder and organizer, AI for Math勉強会 — A seminar series on the use of AI in mathematical research, from mathematicians’ perspectives. Responsible for the overall design of the series.
  4 June 2026: Organized the first AI for Math meeting (hybrid; approximately 43 participants).
  17 July 2026: Organized the second AI for Math meeting (hybrid; 46 registrants, including 29 registered for in-person participation).
  22 October 2026: Planned: the third AI for Math meeting.
• Organizing committee member, JCGTW
• 21 July 2026 – 23 July 2026Attended ZMC Conference 2026: Arithmetic geometry, AI, and Lean.
• Peer-reviewed one manuscript for Applied Categorical Structures.