A categorical semantics of higher order store

We give a categorical description of a class of sound and adequate models of a functional language with assignable variables. This is based on a notion of "sequoidal category", a symmetric monoidal category with an additional non-commutative and non-associative tensor product. We describe a category script G sign of games and strategies, and show that it satisfies our axioms. We give an axiomatic characterization of those categories (including script G sign) which give rise to fully abstract models.