On the triangulated structure of stable monomorphism categories
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915953465360384 |
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| author | Frank, Jonas Schulze, Mathias |
| author_facet | Frank, Jonas Schulze, Mathias |
| contents | We investigate the triangulated structure of stable monomorphism categories (filtered chain categories) over a Frobenius category. The high degree of symmetry of linear quivers leads to a plethora of semiorthogonal decompositions into smaller categories of the same type. These form polygons of recollements, in which a full turn of mutations is a power of a particular auto-equivalence of the stable monomorphism category. A certain power of this auto-equivalence is the square of the suspension functor. We describe the infinite chains of adjoint pairs obtained from the polygons. As an application, we explicate the construction of Bondal and Kapranov for lifting representing objects of dualized hom-functors in our setup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the triangulated structure of stable monomorphism categories Frank, Jonas Schulze, Mathias Category Theory Representation Theory 18G80 (Primary) 18G65, 16G20 (Secondary) We investigate the triangulated structure of stable monomorphism categories (filtered chain categories) over a Frobenius category. The high degree of symmetry of linear quivers leads to a plethora of semiorthogonal decompositions into smaller categories of the same type. These form polygons of recollements, in which a full turn of mutations is a power of a particular auto-equivalence of the stable monomorphism category. A certain power of this auto-equivalence is the square of the suspension functor. We describe the infinite chains of adjoint pairs obtained from the polygons. As an application, we explicate the construction of Bondal and Kapranov for lifting representing objects of dualized hom-functors in our setup. |
| title | On the triangulated structure of stable monomorphism categories |
| topic | Category Theory Representation Theory 18G80 (Primary) 18G65, 16G20 (Secondary) |
| url | https://arxiv.org/abs/2502.20942 |