Idempotent completion of pretriangulated categories

Jichun Liu; Longgang Sun

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 2, page 477-494
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Liu, Jichun, and Sun, Longgang. "Idempotent completion of pretriangulated categories." Czechoslovak Mathematical Journal 64.2 (2014): 477-494. <http://eudml.org/doc/262007>.

@article{Liu2014,
abstract = {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.},
author = {Liu, Jichun, Sun, Longgang},
journal = {Czechoslovak Mathematical Journal},
keywords = {idempotent completion; pretriangulated category; torsion pair; idempotent completion; pretriangulated category; torsion pair},
language = {eng},
number = {2},
pages = {477-494},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Idempotent completion of pretriangulated categories},
url = {http://eudml.org/doc/262007},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Liu, Jichun
AU - Sun, Longgang
TI - Idempotent completion of pretriangulated categories
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 477
EP - 494
AB - 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.
LA - eng
KW - idempotent completion; pretriangulated category; torsion pair; idempotent completion; pretriangulated category; torsion pair
UR - http://eudml.org/doc/262007
ER -

References

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