2021/10/12 by Mikhail V. Bondarko, Bondarko, Mikhail V., С. В. Востоков +1
Computer Science · Mathematics · #18G80 18E40 18G25 55P42 55P91 55N91 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2110.05898
openalex publication_date 2021/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to morphisms killing weights in a range (as defined by the first author) and to objects without these weights (as essentially defined by J. Wildeshaus) in a triangulated category endowed with a weight structure w. We describe several new criteria for morphisms and objects to satisfy these conditions. In some of them we use virtual t-truncations and a t-structure adjacent to w. In the case where the latter exists we prove that a morphism kills weights m,...,n if and only if it factors through an object without these weights; we also construct new families of torsion theories and projective and injective classes. As a consequence, we obtain some "weakly functorial decompositions" of spectra (in the stable homotopy category SH) and a new description of those morphisms that act trivially on degree zero singular cohomology with coefficients in every abelian group.