Soichiro Fujii

I am interested in category theory and its applications. More specifically, I have worked on the following topics.

• Categorical universal algebra.

• Enriched category theory.

• 2-category theory.

• Weak higher-dimensional categories in the sense of Batanin and Leinster.

• Enriched categorical approach to metric spaces and related structures (quantale-enriched categories).

• Graded monads.

[Google Scholar] [arXiv]

1. Towards a formal theory of graded monads. (With Shin-ya Katsumata and Paul-André Melliès) Proceedings of the 19th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2016), Lecture Notes in Computer Science, 9634:513–530, 2016. [doi]

2. Enriched and internal categories: an extensive relationship. (With Thomas Cottrell and John Power) Tbilisi Mathematical Journal, 10(3):239–254, 2017. [doi]

3. Higher dimensional categories: induction on extensivity. (With Thomas Cottrell and John Power) Proceedings of the 34th Conference on the Mathematical Foundations of Programming Semantics (MFPS 2018), Electronic Notes in Theoretical Computer Science, 341:73–90, 2018. [doi]

4. A unified framework for notions of algebraic theory. Theory and Applications of Categories, 34:1246–1316, 2019. [TAC] [arXiv:1904.08541]

5. Completeness and injectivity. Topology and its Applications, 301:107503, 2021. [doi] [arXiv:2005.05311]

6. Quantaloidal approach to constraint satisfaction. (With Yuni Iwamasa and Kei Kimura) Proceedings of the 4th International Conference on Applied Category Theory (ACT 2021), Electronic Proceedings in Theoretical Computer Science, 372:289–305, 2022. [doi] [EPTCS] [arXiv:2107.01778]

7. Hom weak ω-categories of a weak ω-category. (With Thomas Cottrell) Mathematical Structures in Computer Science, 32:420–441, 2022. [doi] [arXiv:2111.00439]

8. Algorithms for coloring reconfiguration under recolorability digraphs. (With Yuni Iwamasa, Kei Kimura, and Akira Suzuki) Proceedings of the 33rd International Symposium on Algorithms and Computation (ISAAC 2022), Leibniz International Proceedings in Informatics (LIPIcs), 248:4, 2022. [doi]

9. The oplax limit of an enriched category. (With Stephen Lack) Theory and Applications of Categories, 40:390–412, 2024. [TAC] [arXiv:2211.12122]

10. Weakly invertible cells in a weak ω-category. (With Keisuke Hoshino and Yuki Maehara) Higher Structures, 8(2):386–415, 2024.  [doi] [arXiv:2303.14907]

11. ω-weak equivalences between weak ω-categories. (With Keisuke Hoshino and Yuki Maehara) Advances in Mathematics, 480:110490, 2025. [doi] [arXiv:2406.13240]

12. Homotopy types of Hom complexes of graph homomorphisms whose codomains are cycles. (With Yuni Iwamasa, Kei Kimura, Yuta Nozaki, and Akira Suzuki) Journal of Applied and Computational Topology, 9:21, 2025. [doi] [arXiv:2408.04802]

13. Homotopy types of Hom complexes of graph homomorphisms whose codomains are square-free. (With Kei Kimura and Yuta Nozaki) To appear in European Journal of Combinatorics. [arXiv:2412.19039]

1. The familial nature of enrichment over virtual double categories. (With Stephen Lack) [arXiv:2507.05529]

1. Enriched categories and tropical mathematics. [arXiv:1909.07620]

2. Introduction to universal algebra and clones. [arXiv:2004.10983]

3. Ordered semirings and subadditive morphisms. [arXiv:2311.03862]

• Foundations of Algebraic Theories and Higher Dimensional Categories. PhD thesis, The University of Tokyo, 2019. [arXiv:1903.07030]

• A 2-Categorical Study of Graded and Indexed Monads. Master's thesis, The University of Tokyo, 2016. [arXiv:1904.08083]

• A Categorical Approach to L-Convexity. Bachelor's thesis, The University of Tokyo, 2014. [arXiv:1904.08413]

• Family name: Fujii /ɸudʒiː/ (in kanji, 藤井) 

• Given name: Soichiro /soːitʃroː/ (in kanji, 宗一郎) 

• Preferred gender pronouns: he, him, his

• Education

  • Apr. 2010–Mar. 2014 Undergraduate course at the Department of Mathematical Engineering and Information Physics, School of Engineering, The University of Tokyo, Japan

  • Apr. 2014–Mar. 2016 Master's course at the Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Japan

  • Apr. 2016–Mar. 2019 PhD course at  the Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Japan

• Employment

  • Apr. 2019–Jul. 2022 Researcher at Research Institute for Mathematical Sciences, Kyoto University, Japan

  • Aug. 2022–Aug. 2024 Visiting Fellow (as a JSPS Overseas Research Fellow) at the School of Mathematical and Physical Sciences, Macquarie University, Australia

  • Sep. 2024–Aug. 2025 Researcher at the Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Czech Republic

  • Sep. 2025– Project Researcher at the National Institute of Informatics, Japan

• CV: [PDF file on Google Drive]

• Email: s.fujii.math [at] gmail.com