Game semantics for free cartesian closed categories

Ruben Zilibowitz – 27 July 2022

One may define various symmetric closed monoidal categories where games are objects and winning strategies, defined on the internal hom objects, are morphisms. Here we examine the special case of free cartesian closed categories and the associated game semantics. Although it is "folklore" that a game semantics for free CCCs does exist, there has not been a very concise account of this in the literature so far. In this talk I will explain the ideas involved and demonstrate a somewhat novel approach to the topic. Time permitting, I will hint at how this approach could be extended to include finite coproducts.