The 2-Deligne Tensor Product
Thibault D. D\'ecoppet
TL;DR
This paper establishes the existence and properties of the 2-Deligne tensor product for compact semisimple 2-categories, extending tensor product theory to higher categorical structures.
Contribution
It proves the existence of the 2-Deligne tensor product for compact semisimple 2-categories and describes its structure under certain conditions.
Findings
Existence of the 2-Deligne tensor product for compact semisimple 2-categories
Description of Hom-categories, connected components, and simple objects
The 2-Deligne tensor product preserves compact semisimplicity
Abstract
We prove that the 2-Deligne tensor product of two compact semisimple 2-categories exists. Further, under suitable hypotheses, we explain how to describe the -categories, connected components, and simple objects of a 2-Deligne tensor product. Finally, we prove that the 2-Deligne tensor product of two compact semisimple tensor 2-categories is a compact semisimple tensor 2-category.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Operator Algebra Research