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Verdier quotients of homotopy categories
- Publication Year :
- 2017
-
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 $x\in\{\infty, +,-,b\}$, and $y\in\{\emptyset,b,+,-,\infty\}$ 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.
- Subjects :
- Mathematics - Representation Theory
18E30 (Primary) 16G10, 16G60 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1711.05445
- Document Type :
- Working Paper