2023/03/21 by Rina Anno, Anno, Rina, Timothy Logvinenko +1
Mathematics · #18G35 (primary) #18G70 #18G80 #18M05 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2303.11796
openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define unbounded twisted complexes and bicomplexes generalising the notion of a (bounded) twisted complex over a DG category [BK90]. These need to be considered relative to another DG category B admitting countable direct sums and shifts. The resulting DG category of unbounded twisted complexes has a fully faithful convolution functor into Mod-B which filters through B if the latter admits change of differential. As an application, we rewrite definitions of A∞-structures in terms of twisted complexes to make them work in an arbitrary monoidal DG category or a DG bicategory.