An Invitation to Game Comonads

Abstract

Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fraïssé games. Remarkably, the categories of coalgebras for these comon-ads capture preservation of several fragments of resource-bounded logics, such as (infinitary) first-order logic with n variables or bounded quantifier rank, and corresponding combinatorial parameters such as tree-width and tree-depth. In this way, game comonads provide a new bridge between categorical methods developed for semantics, and the combinatorial and algorithmic methods of resource-sensitive model theory.