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 language | English |
|---|---|
| Pages (from-to) | 328-373 |
| Number of pages | 46 |
| Journal | Theory and Applications of Categories |
| Volume | 38 |
| Issue number | 12 |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022, Mount Allison University. All rights reserved.
Funding
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.
| Funders | Funder number |
|---|---|
| National Science Foundation (NSF) | DMS-2052923, DMS-1810779, DMS-2005524 |
| University of Kentucky |
Keywords
- Bicategories
- Bicategories with shadows
- Coherence
- Lax monoidal functors
- Lax shadow functors
- Monoidal categories
ASJC Scopus subject areas
- Mathematics (miscellaneous)