Strongly ribbon category

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A strongly ribbon category is a ribbon category $\mathbb{C}$ equipped with a dagger structure such that the functor $\dagger : \mathbb{C}^{op} \rightarrow \mathbb{C}$ coherently preserves the ribbon structure.

[edit] References

S. Abramsky and B. Coecke, A categorical semantics of quantum protocols, Proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS'04). IEEE Computer Science Press (2004).
E.O. Paquette, A categorical semantics for topological quantum computation, Master's thesis, University of Ottawa (2004).