A poisonous example to explicit resolutions of unbounded complexes
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914081937555456 |
|---|---|
| author | Herbera, Dolors Pitsch, Wolfgang Saorín, Manuel Virili, Simone |
| author_facet | Herbera, Dolors Pitsch, Wolfgang Saorín, Manuel Virili, Simone |
| contents | We show that various methods for explicitly building resolutions of unbounded complexes in fact fail when applied to a rather simple and explicit complex. We show that one way to rescue these methods is to assume Roos (Ab.4$^*$)-$k$ axiom, which we adapt to encompass also resolutions in the framework of relative homological algebra. In the end we discuss the existence of model structures for relative homological algebra for unbounded complex under the relative (Ab.4$^*$)-$k$ condition, and present a variety of examples where our results apply. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09741 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A poisonous example to explicit resolutions of unbounded complexes Herbera, Dolors Pitsch, Wolfgang Saorín, Manuel Virili, Simone Rings and Algebras K-Theory and Homology Representation Theory Primary 18G25, Secondary 18E10, 18G10 We show that various methods for explicitly building resolutions of unbounded complexes in fact fail when applied to a rather simple and explicit complex. We show that one way to rescue these methods is to assume Roos (Ab.4$^*$)-$k$ axiom, which we adapt to encompass also resolutions in the framework of relative homological algebra. In the end we discuss the existence of model structures for relative homological algebra for unbounded complex under the relative (Ab.4$^*$)-$k$ condition, and present a variety of examples where our results apply. |
| title | A poisonous example to explicit resolutions of unbounded complexes |
| topic | Rings and Algebras K-Theory and Homology Representation Theory Primary 18G25, Secondary 18E10, 18G10 |
| url | https://arxiv.org/abs/2407.09741 |