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Template Games, Simple Games, and Day Convolution

Authors Clovis Eberhart, Tom Hirschowitz, Alexis Laouar

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Author Details

Clovis Eberhart
  • National Institute of Informatics, Tokyo, Japan
Tom Hirschowitz
  • Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000, Chambéry, France
Alexis Laouar
  • Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000, Chambéry, France

Funding

  • Eberhart, Clovis: ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603, http://dx.doi.org/10.13039/501100009024), JST.

Cite AsGet BibTex

Clovis Eberhart, Tom Hirschowitz, and Alexis Laouar. Template Games, Simple Games, and Day Convolution. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSCD.2019.16

Abstract

Template games [P.-A. Melliès, 2019] unify various approaches to game semantics, by exhibiting them as instances of a double-categorical variant of the slice construction. However, in the particular case of simple games [R. Harmer et al., 2007; C. Jacq and P.-A. Melliès, 2018], template games do not quite yield the standard (bi)category. We refine the construction using factorisation systems, obtaining as an instance a slight generalisation of simple games and strategies. This proves that template games have the descriptive power to capture combinatorial constraints defining well-known classes of games. Another instance is Day’s convolution monoidal structure on the category of presheaves over a strict monoidal category [B. Day, 1970], which answers a question raised in [C. Eberhart, 2018].

Subject Classification

ACM Subject Classification
  • Theory of computation → Denotational semantics
Keywords
  • Game semantics
  • Day convolution
  • Categorical semantics

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References

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