# Ryuya Hora

> Profile of Ryuya Hora (洞龍弥), assistant professor at ZEN University working on topos theory and category theory.

Assistant Professor, ZEN University. Research: topos theory, coalgebras, category theory.
Contact: ryuya_hora@zen.ac.jp, horaryuya38@gmail.com. Last built 2026-08-30.

## Pages
- [Home](https://ryuyahora.jp/)
- [Writings](https://ryuyahora.jp/writings/)
- [Talks](https://ryuyahora.jp/talks/)
- [Activities](https://ryuyahora.jp/activities/)
- [Misc](https://ryuyahora.jp/misc/)
- [CV](https://ryuyahora.jp/cv/)

## Data (JSON, the same source the pages are built from)
- [profile](https://ryuyahora.jp/content/profile.json)
- [writings](https://ryuyahora.jp/content/writings.json) — papers, in preparation, expository
- [talks](https://ryuyahora.jp/content/talks.json)
- [activities](https://ryuyahora.jp/content/activities.json)
- [places](https://ryuyahora.jp/content/places.json)
- [misc](https://ryuyahora.jp/content/misc.json)
- [feed](https://ryuyahora.jp/feed.json) — JSON Feed of papers and talks

## Papers
- Solution to Lawvere's first problem: A Grothendieck topos that has proper class many quotient topoi (Advances in Mathematics 487, 110751, 2026) — https://ryuyahora.jp/writings/#lawvere-first-problem
- 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) — https://ryuyahora.jp/writings/#grothendieck-topoi-left-adjoint
- Normalization of a subgroup, in a topos, and of a word-congruence (arXiv:2511.05012, 2025) — https://ryuyahora.jp/writings/#normalization-subgroup-word-congruence
- Games as recursive coalgebras: A categorical view on the Nim-sum (arXiv:2510.22886, 2025) — https://ryuyahora.jp/writings/#games-recursive-coalgebras
- Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets (arXiv:2503.03439, 2025) — https://ryuyahora.jp/writings/#lawvere-fourth-open-problem
- Topoi of automata I: Four topoi of automata and regular languages (arXiv:2411.06358, 2024) — https://ryuyahora.jp/writings/#topoi-of-automata-i
- Internal parameterization of hyperconnected quotients (Theory and Applications of Categories 42(11), 263-313, 2024) — https://ryuyahora.jp/writings/#internal-parameterizations
- Quotient toposes of discrete dynamical systems (Journal of Pure and Applied Algebra 228(8), 107657, 2024) — https://ryuyahora.jp/writings/#quotient-toposes-discrete-dynamical-systems

## Profiles
- ORCID: https://orcid.org/0009-0008-6975-8908
- researchmap: https://researchmap.jp/ryuyahora?lang=en
- arXiv: https://arxiv.org/search/math?query=Hora%2C+Ryuya&searchtype=author&abstracts=show&order=-announced_date_first&size=50
- nLab: https://ncatlab.org/nlab/show/Ryuya+Hora