| Title:
|
A note on model structures on arbitrary Frobenius categories (English) |
| Author:
|
Li, Zhi-wei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
329-337 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\mathcal {F}$ such that the homotopy category of this model structure is equivalent to the stable category $\underline {\mathcal {F}}$ as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When $\mathcal {F}$ is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed) model structure in the sense of Gillespie (2011). (English) |
| Keyword:
|
Frobenius categorie |
| Keyword:
|
triangulated categories |
| Keyword:
|
model structure |
| MSC:
|
18E10 |
| MSC:
|
18E30 |
| MSC:
|
18E35 |
| idZBL:
|
Zbl 06738522 |
| idMR:
|
MR3661044 |
| DOI:
|
10.21136/CMJ.2017.0582-15 |
| . |
| Date available:
|
2017-06-01T14:25:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146759 |
| . |
| Reference:
|
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