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A Note on the Grothendieck Group of an Additive Category (1109.2040v1)
Published 9 Sep 2011 in math.CT and math.QA
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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