License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2019.16
URN: urn:nbn:de:0030-drops-105237
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10523/
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Eberhart, Clovis ; Hirschowitz, Tom ; Laouar, Alexis

Template Games, Simple Games, and Day Convolution

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LIPIcs-FSCD-2019-16.pdf (0.5 MB)

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].

BibTeX - Entry

@InProceedings{eberhart_et_al:LIPIcs:2019:10523,
  author =	{Clovis Eberhart and Tom Hirschowitz and Alexis Laouar},
  title =	{{Template Games, Simple Games, and Day Convolution}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Herman Geuvers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10523},
  URN =		{urn:nbn:de:0030-drops-105237},
  doi =		{10.4230/LIPIcs.FSCD.2019.16},
  annote =	{Keywords: Game semantics, Day convolution, Categorical semantics}
}

Keywords: Game semantics, Day convolution, Categorical semantics
Collection: 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)
Issue Date: 2019
Date of publication: 18.06.2019

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