# Soichiro Fujii

I am a Visiting Fellow at Macquarie University, supported by the JSPS Overseas Research Fellowships.

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## Research interests

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

Algebraic theories.

Weak higher-dimensional categories à la Batanin and Leinster.

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

Graded monads.

I am also interested in the following topics.

Categorical logic.

Higher-dimensional algebraic theories.

Categorical approach to discrete structures (e.g., matroids).

## Publications

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. [SpringerLink]

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

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. [ScienceDirect]

A unified framework for notions of algebraic theory. Theory and Applications of Categories, 34(40):1246–1316, 2019. [TAC] [arXiv:1904.08541]

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

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]

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]

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]

## Preprints

The oplax limit of an enriched category. (With Stephen Lack) [arXiv:2211.12122]

Weakly invertible cells in a weak ω-category. (With Keisuke Hoshino and Yuki Maehara) [arXiv:2303.14907]

## Notes

Enriched categories and tropical mathematics. [arXiv:1909.07620]

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

Ordered semirings and subadditive morphisms. [arXiv:2311.03862]

## Theses

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]

## Personal information

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

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

Nickname: Ichi /itʃ/

Preferred gender pronouns: he, him, his

Education

April 2007–March 2010 Todaiji Gakuen High School

April 2010–March 2014 Undergraduate course at Department of Mathematical Engineering and Information Physics, School of Engineering, The University of Tokyo

April 2014–March 2016 Master's course at Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo

April 2016–March 2019 PhD course at Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo

Employment

April 2019–July 2022 Researcher at Research Institute for Mathematical Sciences, Kyoto University

August 2022– Visiting Fellow at School of Mathematical and Physical Sciences, Macquarie University (as a JSPS Overseas Research Fellow)

## Contact

Email: s.fujii.math [at] gmail.com