2020/06/10 by Federico Barbacovi, Barbacovi, Federico
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CT #math.RA
paper · pdf · doi:10.48550/arxiv.2006.06016
44 pages, comments are welcome; v2: added funder acknowledgement; v3: 28 pages, main result strengthened: explicit description of the cotwist given, improved exposition, comments are welcome
arxiv created 2021/11/02 · arxiv updated 2021/11/03
E. Segal proved that any autoequivalence of an enhanced triangulated category can be realised as a spherical twist. However, when exhibiting an autoequivalence as a spherical twist one has various choices for the source category of the spherical functor. We describe a construction that realises the composition of two spherical twists as the twist around a single spherical functor whose source category semiorthogonally decomposes into the source categories for the spherical functors we started with. We give a description of the cotwist for this spherical functor and prove, in the special case when our starting twists are around spherical objects, that the cotwist is the Serre functor (up to a shift). We finish with an explicit treatment for the case of P-objects.