On weight complexes, pure functors, and detecting weights

JOURNAL OF ALGEBRA

卷:574

Article

关键词: Triangulated category;    Weight structure;    Weight complex;    Weight-exact functor;    Conservativity;    Motives;    Pure functors;    Equivariant stable homotopy category;    Mackey functors;    Bredon cohomology;   

DOI  :  10.1016/j.jalgebra.2021.02.005

来源: Elsevier

【 摘 要 】

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 wGgenerated 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free