On constructing weight structures and extending them to idempotent\n extensions

2016/05/26 by Mikhail V. Bondarko, Bondarko, Mikhail V., Vladimir Sosnilo +1
Mathematics · #14C15 #18B15 #18E30 #18E40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1605.08372

openalex publication_date 2016/05/26 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28

Abstract

We describe a new method for constructing a weight structure w on a\ntriangulated category C.\n For a given C and w it allow us to give a fairly comprehensive (and new)\ndescription of those triangulated categories consisting of retracts of objects\nof C (i.e., of subcategories of the Karoubi envelope of C that contain C;\nwe call them idempotent extensions of C) such that w extends to them. In\nparticular, any bounded above or below w extends to any idempotent extension\nof C. We also discuss the applications of our results to certain triangulated\ncategories of ("relative") motives.\n

Citations

• On morphisms killing weights, weight complexes, and Eilenberg-Maclane (co)homology of spectra

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• Intersecting the dimension filtration with the slice one for (relative) motivic categories

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