2019/12/04 by Rongmin Zhu, Jiaqun Wei, Zhu, Rongmin +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Business #Category Theory (math.CT) #Computer science #FOS: Mathematics #Geology #Geomorphology #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Siltation #math.CT
paper · pdf · doi:10.48550/arxiv.1912.02111
arXiv admin note: text overlap with arXiv:1707.07353, arXiv:arXiv:1012.2176, arXiv:1705.10981 by other authors
openalex publication_date 2019/12/04 · arxiv created 2019/12/05 · arxiv updated 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let U be a silting object in a derived category over a dg-algebra A, and let B be the endomorphism dg-algebra of U. Under some appropriate hypotheses, we show that if U is good, then there exist a dg-algebra C, a homological epimorphism B→ C and a recollement among the (unbounded) derived categories D(C,d) of C, D(B,d) of B and D(A,d) of A. In particular, the kernel of the left derived functor -⊗^\mathbbLBU is triangle equivalent to the derived category D(C,d). Conversely, if -⊗^\mathbbLBU admits a fully faithful left adjoint functor, then U is good. Moreover, we establish a criterion for the existence of a recollement of the derived category of a dg-algebra relative to two derived categories of weak non-positive dg-algebras. Finally, some applications are given related to good cosilting objects, good 2-term silting complexes, good tilting complexes and modules, which recovers a recent result by Chen and Xi.