In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent form of presheaf semantics and as a concurrent form of game semantics. We define in this setting an analogue of fair testing equivalence, which we prov
e fully abstract w.r.t. standard fair testing equivalence. The proof relies on a new algebraic notion called playground, which represents the `rule of the game. From any playground, we derive two languages equipped with labelled transition systems, as well as a strong, functional bisimulation between them.
We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.
