2023/04/24 by Haïoun, Benjamin · 1 citation
#18M20 #57R56 #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2304.12167
The inclusion of the unit in a braided tensor category V induces a 1-morphism in the Morita 4-category of braided tensor categories BrTens. We give criteria for the dualizability of this morphism. When V is a semisimple (resp. non-semisimple) modular category, we show that the unit inclusion induces under the Cobordism Hypothesis a (resp. non-compact) relative 3-dimensional topological quantum field theory. Following Jordan-Safronov, we conjecture that these relative field theories together with their bulk theories recover Witten-Reshetikhin-Turaev (resp. De Renzi-Gainutdinov-Geer-Patureau-Mirand-Runkel) theories, in a fully extended setting. In particular, we argue that these theories can be obtained by the Cobordism Hypothesis.