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\(K\)-theory for triangulated categories. I(B): Homological functors. (English) Zbl 0906.19003

This is the continuation of [A. Neeman, “\(K\)-theory for triangulated categories. I(A): Homological functors”, Asian J. Math. 1, No. 2, 330-417 (1997; Zbl 0906.19002)]. We use freely the contents and notations of the review of the I(A)-part of the article.
This second part of the article gives a proof of the theorem 4.8, which had already been stated in the I(A)-part: the natural inclusion of the bisimplicial set associated to an abelian category \(\mathcal A\) into the bisimplicial set associated to the category of “graded bounded” objects in \(\mathcal A\) induces a homotopy equivalence.
The proof is technical and relies on the simplicial techniques which have been developed in the I(A)-part.
Reviewer: F.Patras (Nice)

MSC:

19D06 \(Q\)- and plus-constructions
18E30 Derived categories, triangulated categories (MSC2010)

Citations:

Zbl 0906.19002
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