皆様

直前のご案内で申し訳ありません。 明日京都大学にて、新しくポスドクとして来られた Amar Hadzihasanovicさんによる講演があります。 どうぞお気軽にお越しください。

========== Time: 11:00-12:00, 07 Dec, 2017 Place: Rm 478, Research Building 2, Main Campus, Kyoto University 京都大学 本部構内 総合研究2号館 4階478号室 http://www.kyoto-u.ac.jp/en/access/yoshida/main.html (Building 34)

Speaker: Amar Hadzihasanovic (RIMS, Kyoto University)

Title: Units without degeneracies, from higher categories to sequent calculi

In a polycategory or multicategory, the existence of poly-cells or multi-cells satisfying certain universal properties induces coherent algebraic structures on the category of single-input, single-output cells (Cockett-Seely 1997, Hermida 2000). This was used by Hermida to produce an abstract proof of the strictification theorem for monoidal categories, and more generally bicategories. While the basic strategy seems generalisable, by a result by C. Simpson in 1998, no full strictification is possible for higher-dimensional categories. This seems to be due to problems with the combinatorics of cells with degenerate boundaries, that is, “0-ary” inputs or outputs, which were previously used to obtain units. We show that it is possible to obtain coherent units without degenerate boundaries, by deriving them from “equivalence” cells which satisfy lower-dimensional universal properties. This leads to a weaker semi-strictification theorem, which, however, we hope to generalise to arbitrary dimensions. Since the work of Cockett and Seely on linearly distributive categories, it is known that there is a deep connection between universal properties of cells in polycategories, and the rules of sequent calculi; in this context, units are also notorious for increasing the complexity of proof equivalence. In the last part of this talk, we pose some questions on the logical and computational aspects of our notion of unit, and the non-degeneracy constraint.

------------------------------------------ Kazushige TERUI Research Institute for Mathematical Sciences, Kyoto University. Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, JAPAN. Phone: +81-75-753-7235 Fax: +81-75-753-7276 [email protected] http://www.kurims.kyoto-u.ac.jp/~terui/