Geodesic
A note on the Grothendieck group of an additive category
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 17 (2015), pp. 135-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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There are two abelian groups which can naturally be associated to an additive category $\mathcal{A}$: the split Grothendieck group of $\mathcal{A}$ and the triangulated Grothendieck group of the homotopy category of (bounded) complexes in $\mathcal{A}$. We prove that these groups are isomorphic. Along the way, we deduce that the ‘Euler characteristic’ of a complex in $\mathcal{A}$ is invariant under homotopy equivalence, a result which has implications for (de)categorification.
Keywords: Grothendieck group, additive category, categorification. 
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D. Rose. A note on the Grothendieck group of an additive category. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 17 (2015), pp. 135-139. http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a9/

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