Stable Postnikov data of Picard 2-categories

Understand

Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells.

• The classifying space of a Picard 2-category $\mathcal{D}$ is an infinite loop space, the zeroth space of the $K$-theory spectrum $K\mathcal{D}$.
• This spectrum has stable homotopy groups concentrated in levels 0, 1, and 2.
• In this paper, we describe part of the Postnikov data of $K\mathcal{D}$ in terms of categorical structure.