Geodesic
Idempotent completion of pretriangulated categories
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 477-494 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We then prove that the idempotent completion of a pretriangulated category has a natural structure of pretriangulated category. As an application, we show that a torsion pair in a pretriangulated category extends uniquely to a torsion pair in the idempotent completion.
A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We then prove that the idempotent completion of a pretriangulated category has a natural structure of pretriangulated category. As an application, we show that a torsion pair in a pretriangulated category extends uniquely to a torsion pair in the idempotent completion.
DOI : 10.1007/s10587-014-0114-9
Classification : 16B50, 18E05, 18E30, 18E40
Keywords: idempotent completion; pretriangulated category; torsion pair 
@article{10_1007_s10587_014_0114_9,
     author = {Liu, Jichun and Sun, Longgang},
     title = {Idempotent completion of pretriangulated categories},
     journal = {Czechoslovak Mathematical Journal},
     pages = {477--494},
     year = {2014},
     volume = {64},
     number = {2},
     doi = {10.1007/s10587-014-0114-9},
     mrnumber = {3277749},
     zbl = {06391507},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0114-9/}
}
TY  - JOUR
AU  - Liu, Jichun
AU  - Sun, Longgang
TI  - Idempotent completion of pretriangulated categories
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 477
EP  - 494
VL  - 64
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0114-9/
DO  - 10.1007/s10587-014-0114-9
LA  - en
ID  - 10_1007_s10587_014_0114_9
ER  - 
%0 Journal Article
%A Liu, Jichun
%A Sun, Longgang
%T Idempotent completion of pretriangulated categories
%J Czechoslovak Mathematical Journal
%D 2014
%P 477-494
%V 64
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0114-9/
%R 10.1007/s10587-014-0114-9
%G en
%F 10_1007_s10587_014_0114_9
Liu, Jichun; Sun, Longgang. Idempotent completion of pretriangulated categories. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 477-494. doi: 10.1007/s10587-014-0114-9

Cité par Sources :