The higher algebra and geometry of monoidal bicategories
Raffael Stenzel

TL;DR
This paper characterizes braided, sylleptic, and symmetric monoidal bicategories as specific types of $ ext{E}_k$-monoids within a cartesian monoidal $( ext{infinity,1})$-category, using little cubes operads for computational management.
Contribution
It establishes a precise correspondence between certain monoidal bicategories and $ ext{E}_k$-monoids, employing operadic geometry to bridge 2D algebra and $ ext{infinity}$-categorical algebra.
Findings
Braided, sylleptic, and symmetric monoidal bicategories are $ ext{E}_k$-monoids.
Operadic geometry facilitates computations between 2D and $ ext{infinity}$-categorical algebra.
Provides a unified framework for understanding monoidal bicategories via higher algebra.
Abstract
We show that braided, sylleptic and symmetric monoidal bicategories are precisely the -monoids in the cartesian monoidal -category of bicategories for respective integers . 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 -categorical algebra underlying the latter.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
