トポロジー火曜セミナー

過去の記録 ~06/30次回の予定今後の予定 07/01~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河澄 響矢, 北山 貴裕, 逆井卓也, 葉廣和夫
セミナーURL https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2025年07月01日(火)

17:00-18:00   数理科学研究科棟(駒場) hybrid/056号室
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佐藤 玄基 氏 (株式会社 fcuro)
Presentation of finite Reedy categories as localizations of finite direct categories (JAPANESE)
[ 講演概要 ]
In this talk, we present a novel construction that, for a given Reedy category $C$, produces a direct category $\operatorname{Down}(C)$ and a functor $\operatorname{Down}(C) \to C$, exhibiting $C$ as an $(\infty,1)$-categorical localization of $\operatorname{Down}(C)$. This result refines previous constructions in the literature by ensuring that $\operatorname{Down}(C)$ is finite whenever $C$ is finite—a property not guaranteed by existing approaches, such as those by Lurie or by Barwick and Kan. As an intended future application, this finiteness property is expected to be useful for embedding the construction into the syntax of a (non-infinitary) logic. In particular, I expect that the construction may be used to develop a meta-theory of finitely truncated simplicial types and other finite Reedy presheaves for homotopy type theory, thereby extending Kraus and Sattler's unfinished approach. This talk is based on arXiv:2502.05096.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html