Braided -ary coherence conjecture for polyadic tensor categories
Braided -ary coherence conjecture for polyadic tensor categories
Let be a braided semigroupal polyadic category with an -ary tensor product, an -ary associator , and an -ary braiding . Assume that the associator satisfies the -ary coherence conditions giving the canonical reassociation isomorphism on objects, and that the braiding satisfies the polyadic analogue of the hexagon identity. Braided -ary coherence conjecture. Under these assumptions, every diagram containing and commutes.
This is the braided extension of the proposed -ary associator coherence principle, analogous to the role of the hexagon axioms in ordinary braided monoidal categories. The source gives no evidence of a proof or refutation.
Sources & referencesView supporting material
Primary source
Steven Duplij, “Graded medial n-ary algebras and polyadic tensor categories”, arXiv:2001.04165 (2020).
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