Simple free star-autonomous categories and full coherence

Eilenberg-Kelly-MacLane graphs [EK66, KM71] elegantly describe certain morphisms of closed categories. This paper shows that little more is needed to present the free star-autonomous category [Bar79] generated by a category, for a full coherence theorem: the commutativity of diagrams of canonical maps is decidable. Given a set A = {a, b, . . .} of generators, we define the category of A-linkings: objects are star-autonomous shapes (expressions) over A, such as S = ( a⊗ (b ⊗ a) ) ∗∗∗ ⊗ I (with I the unit), and a morphism S → T is a linking, a function from negative leaves to positive leaves, e.g. ( ( I ⊗ I )⊗ ( a⊗ a∗) ) ⊗ ( I ⊗ I∗)