On splitting of morphisms induced by unit map of adjoint functors
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913346222030848 |
|---|---|
| author | Dey, Souvik |
| author_facet | Dey, Souvik |
| contents | Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of (all possible) shifts of an object in the image of the functor. Applications to geometric context related to (derived) splinters and rational singularities are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On splitting of morphisms induced by unit map of adjoint functors Dey, Souvik Algebraic Geometry Commutative Algebra Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of (all possible) shifts of an object in the image of the functor. Applications to geometric context related to (derived) splinters and rational singularities are given. |
| title | On splitting of morphisms induced by unit map of adjoint functors |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2405.06610 |