Hayato Nasu 奈須隼大

I am a master's student at RIMS, Kyoto University, Japan.

I am a member of the Computer Science Group.

Research Interests

I am interested in the following topics:

• Categorical Logic – topos theory, hyperdoctrines, categorical semantics of type theory
• Category Theory – toposes, double categories, higher categories
• Type Theory – homotopy type theory, structural set theory

Preprints on ArXiv

• Double Categories of Relations Relative to Factorisation Systems, with Keisuke Hoshino (2023)
  arXiv:2310.19428
  Abstract

  We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension scheme, and the second focuses on a specific class of vertical arrows defined solely double-categorically. We organise diverse classes of double categories of relations and correlate them with significant classes of factorisation systems. Our framework embraces double categories of spans and double categories of relations on regular categories, which we meticulously compare to existing work on the characterisations of bicategories and double categories of spans and relations.

Talks

• Double categories of Relations Relative to Factorisation Systems given at the Thursday Seminar at RIMS, Kyoto University, on November 16 2023. Slides

• Structural Set Theory -- Towards SEFAR -- the Mathematical Foundations seminar for Young Generation 2023, on December 08 2023. Slides

• (Hyper)doctrines as virtual double categories CSCAT2024 at the University of Chiba, on March 14 2024. Slides

Friends and colleagues

• Keisuke Hoshino RIMS
• Yuto Kawase RIMS
• Ryuya Hora University of Tokyo

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