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Communication Dans Un Congrès Année : 2019

Template Games, Simple Games, and Day Convolution

Clovis Eberhart
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Tom Hirschowitz

Résumé

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].
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Dates et versions

hal-01897309 , version 1 (17-10-2018)
hal-01897309 , version 2 (14-02-2019)
hal-01897309 , version 3 (29-08-2019)

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Clovis Eberhart, Tom Hirschowitz, Alexis Laouar. Template Games, Simple Games, and Day Convolution. 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019), 2019, Dortmund, Germany. pp.16:1--16:19, ⟨10.4230/LIPIcs.FSCD.2019.16⟩. ⟨hal-01897309v3⟩
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