An injective Model for Twisted Derived Categories and Curved Koszul Triality
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912869950423040 |
|---|---|
| author | Hoyer, Yannick Rasmussen, Kristoffer Rank |
| author_facet | Hoyer, Yannick Rasmussen, Kristoffer Rank |
| contents | Given a curved differential graded algebra $A$, we define a new model structure on the category of curved differential graded $A$-modules, called the injective Guan-Lazarev model structure. We prove that the category of CDG $A$-modules with this model structure is Quillen equivalent to the category of curved differential graded contramodules over the extended bar-construction of $A$, equipped with the contraderived model structure. This result can be seen as bridging the gap between Positselski's theory of conilpotent Koszul triality and Guan-Lazarev's work on non-conilpotent Koszul duality. As an application, we use the injective Guan-Lazarev model structure to show that the tensor product is a Quillen bifunctor with respect to these model structures of the second kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An injective Model for Twisted Derived Categories and Curved Koszul Triality Hoyer, Yannick Rasmussen, Kristoffer Rank Category Theory Given a curved differential graded algebra $A$, we define a new model structure on the category of curved differential graded $A$-modules, called the injective Guan-Lazarev model structure. We prove that the category of CDG $A$-modules with this model structure is Quillen equivalent to the category of curved differential graded contramodules over the extended bar-construction of $A$, equipped with the contraderived model structure. This result can be seen as bridging the gap between Positselski's theory of conilpotent Koszul triality and Guan-Lazarev's work on non-conilpotent Koszul duality. As an application, we use the injective Guan-Lazarev model structure to show that the tensor product is a Quillen bifunctor with respect to these model structures of the second kind. |
| title | An injective Model for Twisted Derived Categories and Curved Koszul Triality |
| topic | Category Theory |
| url | https://arxiv.org/abs/2511.03500 |