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Mathematics > K-Theory and Homology

arXiv:1812.11952 (math)
[Submitted on 31 Dec 2018 (v1), last revised 12 Aug 2020 (this version, v4)]

Title:On weight complexes, pure functors, and detecting weights

Authors:Mikhail V. Bondarko
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Abstract:This paper is dedicated to the study of weight complexes (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. For the weight structure $w^G$ 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".
Comments: Several minor corrections made. Appendices (closely related to weight complexes) were extended
Subjects: K-Theory and Homology (math.KT); Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Category Theory (math.CT)
MSC classes: 18E30, 18E40, 14C15, 18G25, 55P42, 55P91 (Primary) 55N91 (Secondary)
Cite as: arXiv:1812.11952 [math.KT]
  (or arXiv:1812.11952v4 [math.KT] for this version)
  https://doi.org/10.48550/arXiv.1812.11952

Submission history

From: Mikhail Bondarko [view email]
[v1] Mon, 31 Dec 2018 18:47:43 UTC (49 KB)
[v2] Mon, 8 Apr 2019 17:54:57 UTC (51 KB)
[v3] Fri, 17 Jan 2020 20:10:32 UTC (58 KB)
[v4] Wed, 12 Aug 2020 23:09:36 UTC (55 KB)
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