Verdier quotients of homotopy categories

2017/11/15 by Guodong Zhou, Alexander Zimmermann, Zhou, Guodong +1
Mathematics · #16G60 (Secondary) #18E30 (Primary) 16G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1711.05445

openalex publication_date 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Verdier quotients of diverse homotopy categories of a full additive subcategory \mathcal E of an abelian category. In particular, we consider the categories K^x,y(\mathcal E) for x∈\∞, +,-,b\, and y∈\∅,b,+,-,∞\ the homotopy categories of left, right, unbounded complexes with homology being 0, bounded, left or right bounded, or unbounded. Inclusion of these categories give a partially ordered set, and we study localisation sequences or recollement diagrams between the Verdier quotients, and prove that many quotients lead to equivalent categories.

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