Coherence for spacial traced categories

Let a spacial traced category be a planar traced category satisfying the spacial and spherical axioms, and consider the graphical language in which diagrams are identified up to isomorphism. Coherence for spacial traced categories. A well-formed equation between morphism terms in the language of spacial traced categories follows from the axioms of spacial traced categories if and only if it holds, up to isomorphism of diagrams, in the graphical language. The graphical language is introduced after spherical traced categories are noted to lack coherence for geometrically useful diagram equivalences; the spacial version is conjectured to restore 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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