Extended TQFTs From Non-Semisimple Modular Categories

Abstract

We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle category of an ETQFT produced by our construction is equivalent to the full subcategory of projective objects of the underlying modular category. In particular, it need not be semisimple.

35 pages, minor changes, references added

References in corpus (2)

• On the Classification of Topological Field Theories
• Modular Categories and TQFTs Beyond Semisimplicity