Abstract

A common intuitive construction of categories of games encodes the basic combinatorics involved in various approaches to the study of games, for example Conway’s recursively structured theory, or the specialised theory of hypergraph games. These ideas have provided some key examples of models of (various fragments of) intuitionistic and linear logic. Such categories have also been used to construct denotational semantics for various abstract programming languages, including the construction of a fully abstract model for PCF .

I’ll begin by outlining how this intuitive construction works. I’ll give an example of such a category (based on bicoloured digraphs) which allows the incorporation of some of the structure of the theory of hypergraph games, and I’ll explain how this construction points to the language of fc-multicategories as a natural setting for the development of additional structure in categories of games. This language also provides a new setting for the construction of existing categories of games. I’ll illustrate how the constructions in this setting have a modular form, cleanly separating different aspects of the underlying combinatorics, and I’ll sketch some possible applications to the development of new constructions.