Coherence for bicategories, lax functors, and shadows

Cary Malkiewich; Kate Ponto

Coherence for bicategories, lax functors, and shadows

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arxiv 2109.01249 v1 pith:UXOQYJDP submitted 2021-09-02 math.CT

Cary Malkiewich , Kate Ponto This is my paper · ORCID

classification math.CT

keywords coherencebicategoriescategoriesfunctorslanemonoidalprooftheorems

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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.

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