The 2-Hilbert Space of a Prequantum Bundle Gerbe

Understand

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion.

• Analogously to usual prequantisation, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space.
• These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes.
• We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian.