The Word Problem for Braided Monoidal Categories is Unknot-Hard

Antonin Delpeuch
(University of Oxford)
Jamie Vicary
(University of Cambridge)

We show that the word problem for braided monoidal categories is at least as hard as the unknotting problem. As a corollary, so is the word problem for Gray categories. We conjecture that the word problem for Gray categories is decidable.

In Kohei Kishida: Proceedings of the Fourth International Conference on Applied Category Theory (ACT 2021), Cambridge, United Kingdom, 12-16th July 2021, Electronic Proceedings in Theoretical Computer Science 372, pp. 72–87.
Published: 3rd November 2022.

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