Dear categorists, Clovis Eberhart and I just uploaded a new preprint, on which we'd be eager to read your constructive comments. https://hal.archives-ouvertes.fr/hal-01634162/document What's in a game? A theory of game models Abstract: Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of strategies. We set out to unify these models into a basic abstract framework for game semantics, game settings. Our main contribution is the generic construction, for any game setting, of a category of games and strategies. Furthermore, we extend the framework to deal with innocence, and prove that innocent strategies form a subcategory. We finally show that our constructions cover many concrete cases, mainly among the early models and the very recent sheaf-based ones. Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]