A Note on the Grothendieck Group of an Additive Category

Details A Note on the Grothendieck Group of an Additive Category A Note on the Grothendieck Group of an Additive Category

2011-09-09

arxiv.org/abs/1109.2040v1

Mathematics

Category Theory

9 pages

Scientific paper

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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