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Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory

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Are the tangle functors based off Khovanov homology braided monoidal functors?

I was wondering if the tangle functors constructed in "A functor-valued invariant of tangles" https://arxiv.org/pdf/math/0103190.pdf "An invariant of tangle cobordisms via subquotients of arc rings" …