COHERENCE FOR BICATEGORIES, LAX FUNCTORS, AND SHADOWS

Cary Malkiewich, Kate Ponto

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)328-373
Number of pages46
JournalTheory and Applications of Categories
Volume38
Issue number12
StatePublished - 2022

Bibliographical note

Funding Information:
CM was supported by the NSF grants DMS-2005524 and DMS-2052923. KP was supported by NSF grants DMS-1810779 and DMS-2052923, and the Royster research professorship at the University of Kentucky.

Publisher Copyright:
© 2022, Mount Allison University. All rights reserved.

Keywords

  • Bicategories
  • Bicategories with shadows
  • Coherence
  • Lax monoidal functors
  • Lax shadow functors
  • Monoidal categories

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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