京都大学数理解析研究所の佐藤です。

4月13日11:00から、東京大学のMarc Bagnol氏に 以下の講演をしていただくことになりましたので、 ご連絡いたします。どうぞお気軽にお越しください。 ========== Time: 11:00-12:00, 13 Apr, 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) http://www.kyoto-u.ac.jp/ja/access/campus/map6r_y.htm (34番の建物)

Speaker: Marc Bagnol (JSPS Postdoctoral Fellow, University of Tokyo)

Title: A Free Trace Construction and the Embedding Problem

Abstract:

The notion of traced category allows to model feedback situations in the language of category theory. Traces are ubiquitous in mathematics and serve as the basis for the categorical formulation of Girard's Geometry of Interaction. The notion was extended to partially-defined traces by Scott and Haghverdi, and a representation theorem was later shown: any partially traced category can be embedded in a fully traced one.

A related problem we are currently investigating with some RIMS members is understanding when a monoidal category can be embedded into a traced one, or equivalently when it can be equipped with a partial trace. This "embedding problem" has already seen a few tentative solutions, conditions that are necessary but turned out not to be sufficient which I will present and discuss.

I will also present a construction of a free trace for monoidal categories that both can be used to prove the representation theorem mentioned above (this was its original purpose) and gives an angle to look at the embedding problem.