Coherence for bicategories, lax functors, and shadows

Cary Malkiewich and Kate Ponto

Coherence theorems are fundamental to how we think about monoidal categories and their generalizations. In this paper we revisit Mac Lane's original proof of coherence for monoidal categories using the Grothendieck construction. This perspective makes the approach of Mac Lane's proof very amenable to generalization. We use the technique to give efficient proofs of many standard coherence theorems and new coherence results for bicategories with shadow and for their functors.

Keywords: coherence, monoidal categories, bicategories, bicategories with shadows, lax monoidal functors, lax shadow functors

2020 MSC: 18M05,18N10

Theory and Applications of Categories, Vol. 38, 2022, No. 12, pp 328-373.

Published 2022-02-24.

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