We revise our `Physical Traces' paper in the light of the results in [Abramsky and Coecke LiCS`04]. The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved. In this paper we improve on the definition of strong compact closure as compared to the one presented in [Abramsky and Coecke LiCS`04]. This modification enables an elegant characterization of strong compact closure in terms of adjoints and a Yanking axiom, and a better treatment of bipartite projectors.
2000 MSC: 15A04,15A90,18B10,18C50,18D10,81P10,81P68
Theory and Applications of Categories,
Vol. 14, 2005,
No. 6, pp 111-124.