Extended TQFTs from non-semisimple modular categories

• DOI: 10.1512/iumj.2021.70.9364
• Publication Date: 2021-11-03T21:44:17Z
• Authors: Marco De Renzi
• Keywords: 10123 Institute of Mathematics; Mathematics - Geometric Topology; 510 Mathematics; FOS: Mathematics; Geometric Topology (math.GT); [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]

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.<br/>35 pages, minor changes, references added<br/>