How strict is strictification?
arXiv:1802.07538 · doi:10.1016/j.jpaa.2018.10.004
Abstract
The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the -category of -categories and the tricategory of bicategories. We show that -- far from requiring the full weakness provided by the definitions of tricategory theory -- this adjunction can be enriched over the symmetric closed multicategory of bicategories defined by Verity. Moreover, we show that this adjunction underlies an adjunction of bicategory-enriched symmetric multicategories. An appendix introduces the symmetric closed multicategory of pseudo double categories, into which Verity's symmetric multicategory of bicategories embeds fully.
arXiv comment26 pages; v2. final version, to appear in J. Pure Appl. Algebra
References in corpus (13)
- A 2-categories companion
- A Quillen model structure for Gray-categories
- Icons
- Homotopy-theoretic aspects of 2-monads
- Permutative categories, multicategories, and algebraic K-theory
- Model Structures on the Category of Small Double Categories
- Skew monoidal categories and skew multicategories
- The low-dimensional structures formed by tricategories
- Closed categories vs. closed multicategories
- Bicat is not triequivalent to Gray
- Relative symmetric monoidal closed categories I: Autoenrichment and change of base
- The monoidal structure of strictification
- Braided skew monoidal categories