Categorical Combinatorics for Innocent Strategies

@article{Harmer2007CategoricalCF,
  title={Categorical Combinatorics for Innocent Strategies},
  author={Russell Harmer and Martin Hyland and Paul-Andr{\'e} Melli{\`e}s},
  journal={22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)},
  year={2007},
  pages={379-388}
}
We show how to construct the category of games and innocent strategies from a more primitive category of games. On that category we define a comonad and monad with the former distributing over the latter. Innocent strategies are the maps in the induced two-sided Kleisli category. Thus the problematic composition of innocent strategies reflects the use of the distributive law. The composition of simple strategies, and the combinatorics of pointers used to give the comonad and monad are… CONTINUE READING
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