Coherence for planar traced categories

Let a planar traced category be a monoidal category equipped with right and left traces satisfying the three additional axioms of interchange, left pivoting, and right pivoting, and interpret its graphical language up to planar isotopy. Coherence for planar traced categories. A well-formed equation between morphism terms in the language of planar traced categories follows from the axioms of planar traced categories if and only if it holds in the graphical language up planar isotopy. The axioms are stated to be sound; this conjecture asserts completeness, and the source gives no resolution.

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Primary source

Peter Selinger, “A survey of graphical languages for monoidal categories”, arXiv:0908.3347 (2009).

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