Complicial simple-minded collections
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910071957487616 |
|---|---|
| author | Plogmann, Marvin |
| author_facet | Plogmann, Marvin |
| contents | We consider the problem of characterizing derived endomorphism algebras of simple objects in length categories up to quasi-isomorphism. We give such a characterization for module categories, abelian categories, exact categories, as well as, for certain differential graded analogues of them. It turns out that the property of being $d$-complicial ($d\geq 1$), in the sense of Lurie, of the involved simple-minded collections plays a central role. We also explain how this characterization can be interpreted as a coherent generation property for any minimal $A_{\infty}$-model of the derived endomorphism algebra. Along the way, we propose a notion of length exact differential graded categories and explain how they relate to length abelian $d$-truncated differential graded categories, generalizing results of Enomoto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03122 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complicial simple-minded collections Plogmann, Marvin Representation Theory Primary: 18G80. Secondary: 18G35 We consider the problem of characterizing derived endomorphism algebras of simple objects in length categories up to quasi-isomorphism. We give such a characterization for module categories, abelian categories, exact categories, as well as, for certain differential graded analogues of them. It turns out that the property of being $d$-complicial ($d\geq 1$), in the sense of Lurie, of the involved simple-minded collections plays a central role. We also explain how this characterization can be interpreted as a coherent generation property for any minimal $A_{\infty}$-model of the derived endomorphism algebra. Along the way, we propose a notion of length exact differential graded categories and explain how they relate to length abelian $d$-truncated differential graded categories, generalizing results of Enomoto. |
| title | Complicial simple-minded collections |
| topic | Representation Theory Primary: 18G80. Secondary: 18G35 |
| url | https://arxiv.org/abs/2603.03122 |