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Coherence for Categorified Operadic Theories

Miles Gould
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Abstract

It has long been known that every weak monoidal category A is equivalent via monoidal functors and monoidal natural transformations to a strict monoidal category st(A). We generalise the definition of weak monoidal category to give a definition of weak P-category for any strongly regular (operadic) theory P, and show that every weak P-category is equivalent via P-functors and P-transformations to a strict P-category. This strictification functor is then shown to have an interesting universal property.

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Miles Gould. 2006-07-18. Coherence for Categorified Operadic Theories. https://arxiv.org/abs/math/0607423

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