The naturality of twist

Ross Street – 17 June 1998

While working on her Honours Essay, Amy Young noticed that our paper A. Joyal, R. Street and D. Verity, Traced monoidal categories, Mathematical Proceedings of the Cambridge Philosophical Society 119 (3) (1996) 425-446; MR96m:18014 did not include a proof that the twist on the tortile monoidal category Int(V), constructed from a traced monoidal category V, was natural. The equality between string diagrams expressing this naturality is not so obvious so I explained the algebraic proof. Amy's Essay includes a nicely drawn geometric proof.