A Note on the Grothendieck Group of an Additive Category
Category Theory
2011-09-12 v1 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1109.2040,
title = {A Note on the Grothendieck Group of an Additive Category},
author = {David E. V. Rose},
journal= {arXiv preprint arXiv:1109.2040},
year = {2011}
}
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9 pages