Induced complete hereditary cotorsion pairs in D(R) with respect to Cartan-Eilenberg exact sequences
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911316615102464 |
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| author | Yang, Xiaoyan |
| author_facet | Yang, Xiaoyan |
| contents | Given a complete hereditary cotorsion pair (A,B) in ModR, we construct a complete hereditary cotorsion pair in the derived category D(R) of unbounded complexes with respect to the proper class ξ of cohomologically ghost triangles induced by the Cartan-Eilenberg exact sequences. More specifically, we prove that, each of the classes of projectively coresolved ξ-Gflat complexes PGF(ξ), ξ-Gflat complexes GF(ξ), ξ-Ginjective complexes GI(ξ), ξ-Gprojective complexes GP(ξ) (the last when R is virtually Gorenstein), forms one half of a complete hereditary cotorsion pair in D(R) with respect to ξ. Moreover, various homological dimensions offer additional way to obtain such cotorsion pairs in D(R) with respect to ξ. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Induced complete hereditary cotorsion pairs in D(R) with respect to Cartan-Eilenberg exact sequences Yang, Xiaoyan Category Theory Given a complete hereditary cotorsion pair (A,B) in ModR, we construct a complete hereditary cotorsion pair in the derived category D(R) of unbounded complexes with respect to the proper class ξ of cohomologically ghost triangles induced by the Cartan-Eilenberg exact sequences. More specifically, we prove that, each of the classes of projectively coresolved ξ-Gflat complexes PGF(ξ), ξ-Gflat complexes GF(ξ), ξ-Ginjective complexes GI(ξ), ξ-Gprojective complexes GP(ξ) (the last when R is virtually Gorenstein), forms one half of a complete hereditary cotorsion pair in D(R) with respect to ξ. Moreover, various homological dimensions offer additional way to obtain such cotorsion pairs in D(R) with respect to ξ. |
| title | Induced complete hereditary cotorsion pairs in D(R) with respect to Cartan-Eilenberg exact sequences |
| topic | Category Theory |
| url | https://arxiv.org/abs/2512.12096 |