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arXiv · 1711.05445

Verdier quotients of homotopy categories

Guodong Zhou·Alexander Zimmermann
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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.

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Guodong Zhou, Alexander Zimmermann. 2017-11-15. Verdier quotients of homotopy categories. https://arxiv.org/abs/1711.05445

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