Geodesic
A note on the Grothendieck group of an additive category
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 17 (2015), pp. 135-139

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{VCHGU_2015_17_a9,
     author = {D. Rose},
     title = {A note on the {Grothendieck} group of an additive category},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {135--139},
     publisher = {mathdoc},
     number = {17},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a9/}
}
TY  - JOUR
AU  - D. Rose
TI  - A note on the Grothendieck group of an additive category
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2015
SP  - 135
EP  - 139
IS  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a9/
LA  - en
ID  - VCHGU_2015_17_a9
ER  - 
%0 Journal Article
%A D. Rose
%T A note on the Grothendieck group of an additive category
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2015
%P 135-139
%N 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VCHGU_2015_17_a9/
%G en
%F VCHGU_2015_17_a9
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/