Categorical matrix factorizations and monomorphism categories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918493160472576 |
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| author | Frank, Jonas Schulze, Mathias |
| author_facet | Frank, Jonas Schulze, Mathias |
| contents | This article generalizes the correspondence between matrix factorizations and maximal Cohen-Macaulay modules over hypersurface rings due to Eisenbud and Yoshino. We consider factorizations with several factors in a purely categorical context, extending results of Sun and Zhang for Gorenstein projective module factorizations. Our formulation relies on a notion of hypersurface category and replaces Gorenstein projectives by objects of general Frobenius exact subcategories. We show that factorizations over such categories form again a Frobenius category. Our main result is then a triangle equivalence between the stable category of factorizations and that of chains of monomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical matrix factorizations and monomorphism categories Frank, Jonas Schulze, Mathias Category Theory Commutative Algebra 18G50, 18G65 (Primary) 18G80, 16E65 (Secondary) This article generalizes the correspondence between matrix factorizations and maximal Cohen-Macaulay modules over hypersurface rings due to Eisenbud and Yoshino. We consider factorizations with several factors in a purely categorical context, extending results of Sun and Zhang for Gorenstein projective module factorizations. Our formulation relies on a notion of hypersurface category and replaces Gorenstein projectives by objects of general Frobenius exact subcategories. We show that factorizations over such categories form again a Frobenius category. Our main result is then a triangle equivalence between the stable category of factorizations and that of chains of monomorphisms. |
| title | Categorical matrix factorizations and monomorphism categories |
| topic | Category Theory Commutative Algebra 18G50, 18G65 (Primary) 18G80, 16E65 (Secondary) |
| url | https://arxiv.org/abs/2504.06052 |