The pebbling comonad in Finite Model Theory

@article{Abramsky2017ThePC,
  title={The pebbling comonad in Finite Model Theory},
  author={S. Abramsky and A. Dawar and Pengming Wang},
  journal={2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  year={2017},
  pages={1-12}
}
Pebble games are a powerful tool in the study of finite model theory, constraint satisfaction and database theory. Monads and comonads are basic notions of category theory which are widely used in semantics of computation and in modern functional programming. We show that existential k-pebble games have a natural comonadic formulation. Winning strategies for Duplicator in the k-pebble game for structures A and B are equivalent to morphisms from A to B in the coKleisli category for this comonad… Expand
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