The higher algebra and geometry of monoidal bicategories
Abstract
We show that braided, sylleptic and symmetric monoidal bicategories are precisely the $\mathsf{E}_k$-monoids in the cartesian monoidal $(\infty,1)$-category of bicategories for respective integers $k$. To manage the underlying computations, we use the geometry of the little cubes operads to mediate between the 2-dimensional algebra underlying the former and the $\infty$-categorical algebra underlying the latter.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 16 February 2026
- Language
- EN
- Document type
- Preprint