Constructing symmetric monoidal bicategories

By Michael Shulman. 2010

76 citations recorded by the source corpus.

We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely applicable, though not universally so.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26451c9ff429037294edd93bba41b4fa8e78ae3d

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Shadows and traces in bicategories (2009, background): “ ⋆ M form a “lax natural transformation.” We call this a conjunctional transformation because it is a “conjoint pair” in the double category of lax and oplax natural transformations; see for instance [34]. Before we can state and prove an analogue of Proposition 2.13, we need one further observation”
The higher Morita category of n–algebras (2014, background): “e “ ∞-version” of 2Although it is intuitively clear that the tensor product on C induces such a symmetric monoidalstructure, this seems to have been completelydeﬁn ed only quite recentlyby Shulman in [40], following a construction of a braided monoidal structure by Garner and Gurski in [15]. Conside”
The Classification of Two-Dimensional Extended Topological Field Theories (2011, background): “−1)-manifold without corners or boundary (but possibly non-compact) and B is a d-manifold without corners or boundary. Halations for Y are partially ordered with partial order given by diagrams, 1See [Shu10] for an intriguing alternative approach to this result. 3.2. THE BORDISM BICATEGORY II: HALOS”