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arXiv · 1109.2040

A Note on the Grothendieck Group of an Additive Category

David E. V. Rose
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Abstract

There are two abelian groups which can naturally be associated to an additive category A: the split Grothendieck group of A and the triangulated Grothendieck group of the homotopy category of (bounded) complexes in A. We prove that these groups are isomorphic. Along the way, we deduce that the `Euler characteristic' of a complex in A is invariant under homotopy equivalence.

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David E. V. Rose. 2011-09-09. A Note on the Grothendieck Group of an Additive Category. https://arxiv.org/abs/1109.2040

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