The Category of Operator Spaces and Complete Contractions

Abstract

We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable. This result, together with its symmetric monoidal closed structure with respect to the projective tensor product of operator spaces, implies the existence of cofree (cocommutative) coalgebras with respect to the projective tensor product and therefore provides a mathematical model of Intuitionistic Linear Logic in the sense of Lafont.