2023/12/07 by Kevin Coulembier, Pavel Etingof, Coulembier, Kevin +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2312.03972
openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply the recently introduced notion, due to Dyckerhoff, Kapranov and Schechtman, of N-spherical functors of stable infinity categories, which generalise spherical functors, to the setting of monoidal categories. We call an object N-bounded if the corresponding regular endofunctor on the derived category is N-spherical. Besides giving new examples of N-spherical functors, the notion of N-bounded objects gives surprising connections with Jones-Wenzl idempotents, Frobenius-Perron dimensions and central conjectures in the field of symmetric tensor categories in positive characteristic.