An introduction to monomorphism categories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913443926245376 |
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| author | Kvamme, Sondre |
| author_facet | Kvamme, Sondre |
| contents | This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be divided into four parts: The first part is an introduction to the theory of monomorphism categories, including a short survey on some representation theoretic results. The second part is a summary of some recent results on monomorphism categories based on joint work with Nan Gao, Julian Külshammer and Chrysostomos Psaroudakis. It also includes a new result, namely a classification of all monomorphism categories of finite type over cyclic abelian groups. The third part concerns the relationship between submodule categories and $p$-valuated abelian groups. The last part contains a proof of wildness of a certain monomorphism category, rectifying a statement in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An introduction to monomorphism categories Kvamme, Sondre Representation Theory Rings and Algebras 16G70, 16G20, 20K27, 16E65 This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be divided into four parts: The first part is an introduction to the theory of monomorphism categories, including a short survey on some representation theoretic results. The second part is a summary of some recent results on monomorphism categories based on joint work with Nan Gao, Julian Külshammer and Chrysostomos Psaroudakis. It also includes a new result, namely a classification of all monomorphism categories of finite type over cyclic abelian groups. The third part concerns the relationship between submodule categories and $p$-valuated abelian groups. The last part contains a proof of wildness of a certain monomorphism category, rectifying a statement in the literature. |
| title | An introduction to monomorphism categories |
| topic | Representation Theory Rings and Algebras 16G70, 16G20, 20K27, 16E65 |
| url | https://arxiv.org/abs/2407.17147 |