The 2-Deligne Tensor Product

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 $Hom$-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.

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Cited by in corpus (7)

• Finite Semisimple Module 2-Categories
• Fusion 3-Categories for Duality Defects
• Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories
• Compact Semisimple 2-Categories
• On the Dualizability of Fusion 2-Categories
• The Relative Deligne Tensor Product over Pointed Braided Fusion Categories
• Compact Semisimple Tensor 2-Categories are Morita Connected