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The additivity of traces in triangulated categories. (English) Zbl 1007.18012

The author states a theorem on the additivity of the Euler characteristic – or more generally, a suitably defined trace – when applied to distinguished triangles of suitably dualizable objects in a refined notion of triangulated category. The main point of the paper is to write down the axioms needed to make such a theorem true, and to provide examples. The axioms, which seems to be complicated, are satisfied whenever the triangulated category arises as the homotopy category of a stable model category in the sense of M. Hovey [“Model categories”, Math. Surv. Monogr. 63, Am. Math. Soc. (1999; Zbl 0909.55001), Chapter 7]. Most, if not all, important examples of triangulated categories arise under this rubric.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
55N35 Other homology theories in algebraic topology

Citations:

Zbl 0909.55001
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References:

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