The 2-Deligne Tensor Product

Understand

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.