This paper is dedicated to the study of weight complex functors (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that “ignore all non-zero weights”; these have a nice description in terms of weight complexes. An important example is the weight structure wG generated by the orbit category in the G-equivariant stable homotopy category SH(G); the corresponding pure cohomological functors into abelian groups are the Bredon cohomology associated to Mackey functors ones. Pure functors related to “motivic” weight structures are also quite useful. Our results also give some (more) new weight structures. Moreover, we prove that certain exact functors are conservative and “detect weights”.

Original languageEnglish
Pages (from-to)617-668
Number of pages52
JournalJournal of Algebra
Volume574
DOIs
StatePublished - 15 May 2021

    Research areas

  • Bredon cohomology, Conservativity, Equivariant stable homotopy category, Mackey functors, Motives, Pure functors, Triangulated category, Weight complex, Weight structure, Weight-exact functor

    Scopus subject areas

  • Algebra and Number Theory

ID: 75128889