2022/02/15 by Tathagata Basak, Shlomo Gelaki, Basak, Tathagata +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2202.07701
We extend \citeG to the nonsemisimple case. We define and study exact factorizations \B=\A\bullet \C of a finite tensor category \B into a product of two tensor subcategories \A,\C⊂ \B, and relate exact factorizations of finite tensor categories to exact sequences of finite tensor categories with respect to exact module categories \citeEG. We apply our results to study exact factorizations of quasi-Hopf algebras, and extensions of a finite group scheme theoretical tensor category \citeG2 by another one. We also provide several examples to illustrate our results.