2011/07/06 by Olaf M. Schnürer, Schnürer, Olaf M.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #math.AG #math.CT #math.KT #math.RT
paper · pdf · doi:10.48550/arxiv.1107.1227
82 pages, comments welcome
arxiv created 2011/07/06 · openalex publication_date 2011/07/06 · arxiv updated 2011/07/07 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
This article provides some basic results on weight structures, weight complex functors and homotopy categories. We prove that the full subcategories K(A)w < n, K(A)w > n, K(A)- and K(A)+ (of objects isomorphic to suitably bounded complexes) of the homotopy category K(A) of an additive category A are idempotent complete, which confirms that (K(A)w <= 0, K(A)w >= 0) is a weight structure on K(A). We discuss weight complex functors and provide full details of an argument sketched by M. Bondarko, which shows that if w is a bounded weight structure on a triangulated category T that has a filtered triangulated enhancement T' then there exists a strong weight complex functor T -> K(heart(w))anti. Surprisingly, in order to carry out the proof, we need to impose an additional axiom on the filtered triangulated category T' which seems to be new.