Photo taken by Giacomo Tendas

Yuki Maehara（前原 悠究）

日本語版はこちらからどうぞ

email: ymaehar@kurims.kyoto-u.ac.jp

I am a postdoc at Research Institute for Mathematical Sciences, Kyoto University in Japan.
My previous postdoc was at Institute of Mathematics for Industry, Kyushu University.
Before that, I was a PhD student of Dominic Verity and Ross Street at Macquarie University in Sydney, Australia.

I am interested in (higher) category theory.

Here (no. 8) is my 5 minute self-introduction from the Higher Categories and Categorificaction program at the MSRI in spring 2020.

Publications

Category theory

1. ω-weak equivalences between weak ω-categories
   joint with Soichiro Fujii and Keisuke Hoshino
   arxiv:2406.13240
2. A model-independent Gray tensor product for (∞,2)-categories
   joint with Tim Campion
   arXiv:2304.05965
3. Weakly invertible cells in a weak ω-category
   joint with Soichiro Fujii and Keisuke Hoshino
   arXiv:2303.14907
4. Equivalence of cubical and simplicial approaches to (∞,n)-categories
   joint with Brandon Doherty and Chris Kapulkin
   arXiv:2106.09428
   DOI:10.1016/j.aim.2023.108902
5. Orientals as free weak ω-categories
   arXiv:2102.09736
   DOI:10.1016/j.jpaa.2022.107230
6. A cubical model for (∞,n)-categories.
   joint with Tim Campion and Chris Kapulkin
   arxiv:2005.07603
7. The Gray tensor product for 2-quasi-categories
   arXiv:2003.11757
   DOI:10.1016/j.aim.2020.107461
8. Inner horns for 2-quasi-categories
   arXiv:1902.08720
   DOI:10.1016/j.aim.2020.107003

Mahavier limits/generalised inverse limits

• Inverse limits of upper semicontinuous functions and indecomposable continua
  joint with Gareth Davies, Sina Greenwood, and Michael Lockyer
  DOI:10.1016/j.topol.2020.107471
• Mahavier completeness and classifying diagrams
  joint with Ittay Weiss
  ResearchGate
  DOI:10.1016/j.topol.2017.07.007
• Categories of inverse systems of compacta with upper semi-continuous bonding functions
  DOI:10.1016/j.topol.2016.02.007

Other material

• Augmented simplicial sets as M-sets
• Describing groups using first-order language, summer project report.

Talks

Research talks

• Weak equivalences between algebraic weak ω-categories
  • Jun. 2024: Category Theory (University of Santiago de Compostela; slides)
• Equivalences in and between algebraic weak ω-categories
  • Apr. 2024: (∞,n)-Categories and their applications (Utrecht University; slides)
• Coinductive equivalences in algebraic weak ω-categories
  • Jul. 2023: Category Theory (Université catholique de Louvain)
  • Mar. 2023: Workshop on Computer Science and Category Theory (Kyoto University)
  • Dec. 2022: Annual Meeting of the Australian Mathematical Society (University of New South Wales; slides)
  • Nov. 2022: Australian Category Seminar (Macquarie University)
• Equivalence of cubical and simplicial approaches to weak ω-categories
  • Sep. 2021: Seminar on Algebra, Logic and Geometry in Informatics (online; slides)
• Orientals as free weak ω-categories
  • Sep. 2021: Category Theory (University of Genoa; online; slides)
  • Mar. 2021: Workshop on Computer Science and Category Theory (online)
  • Feb. 2021: E8 Sporadic Mathematical Online Lecture Series (online)
  • Feb. 2021: Australian Category Seminar (Macquarie University; online)
• Triangulating weak ω-categories into weak ω-categories
  • Oct. 2020: Geometry and topology seminar (University of Western Ontario; online)
• Augmented simplicial sets as M-sets
  • Jul. 2020: Australian Category Seminar (Macquarie University; online)
• A cubical model for weak ω-categories
  • Oct. 2020: Homotopy Type Theory Electronic Seminar Talks (online; video, slides)
  • Jul. 2020: AG-Seminar (Universität Regensburg; online)
  • Jul. 2020: Geometric and Categorical Structures in Computation and Deduction (Satellite Workshop of Formal Structures for Computation and Deduction; online)
  • Jun. 2020: Australian Category Seminar (Macquarie University; online)
  • May 2020: Mathematical Sciences Research Institute, cubical sets seminar (online; video)
• Towards the formal theory of homotopy coherent monads
  • Feb. 2020: Australian Category Seminar (Macquarie University)
• The Gray tensor product for 2-quasi-categories
  • Dec. 2020: Annual Meeting of the Australian Mathematical Society (University of New England; slides)
  • Feb. 2020: Mathematical Sciences Research Institute, (∞,2)-categories working group
  • Nov. 2019: Australian Category Seminar (Macquarie University)
  • Jul. 2019: Category Theory (University of Edinburgh)
• Inner horns for 2-quasi-categories
  • Mar. 2019: Australian Category Seminar (Macquarie University)
  • Dec. 2018: Annual Meeting of the Australian Mathematical Society (University of Adelaide; slides)
• Mahavier limits
  • Dec. 2017: Annual Meeting of the Australian Mathematical Society (Macquarie University; slides)
• Indecomposable generalised inverse limits
  • Feb. 2014: Devonport Topology Festival; joint talk with Stephen Bell

Expository talks

I (re)started the Junior Category Theory Seminar (to which no "grown-ups" beyond postdocs are invited) at Macquarie University and spoke about the following topics in 2018-2019:

• Cubical sets
• ω-categories, orientals, and complicial sets
• Monads and theories (this paper by Bourke and Garner)
• Inner horns and spines for ∞-categories
• Martin-Löf type theory
• The formal theory of monads (this paper by Street)
• Quasi-categories
• Model categories

Other expository talks I have given include:

• A friendly introduction to ∞-categories
  • Jan.-Feb. 2022: Higher Category Lecture (Australian National University; online; slides from Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, and Lecture 6)
• Introduction to ∞-categories in general and quasi-categories in particular
  • May 2021: Thursday Seminar (Kyoto University; online; slides)
• Associativity without equality
  • Jun. 2019: Department Research Congress (Macquarie University)
• Homotopy theory and model categories
  • Jan. 2015: Summer Scholar Presentation (Australian National University)