| Title:
|
Idempotent completion of pretriangulated categories (English) |
| Author:
|
Liu, Jichun |
| Author:
|
Sun, Longgang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
477-494 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
idempotent completion |
| Keyword:
|
pretriangulated category |
| Keyword:
|
torsion pair |
| MSC:
|
16B50 |
| MSC:
|
18E05 |
| MSC:
|
18E30 |
| MSC:
|
18E40 |
| idZBL:
|
Zbl 06391507 |
| idMR:
|
MR3277749 |
| DOI:
|
10.1007/s10587-014-0114-9 |
| . |
| Date available:
|
2014-11-10T09:51:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144011 |
| . |
| Reference:
|
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