A Computational Approach to the Homotopy Theory of DG categories
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909190944980992 |
|---|---|
| author | Karabas, Dogancan Lee, Sangjin |
| author_facet | Karabas, Dogancan Lee, Sangjin |
| contents | We give a specific cylinder functor for semifree dg categories. This allows us to construct a homotopy colimit functor explicitly. These two functors are "computable", specifically, the constructed cylinder functor sends a dg category of finite type, i.e., a semifree dg category having finitely many generating morphisms, to a dg category of finite type. The homotopy colimit functor has a similar property. Moreover, using the cylinder functor, we give a cofibration category of semifree dg categories and that of dg categories of finite type, independently from the work of Tabuada. All the results similarly work for semifree dg algebras. We also describe an application to symplectic topology and provide a toy example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Computational Approach to the Homotopy Theory of DG categories Karabas, Dogancan Lee, Sangjin Category Theory K-Theory and Homology Symplectic Geometry 18G35, 18N40, 18N45, 53D37 We give a specific cylinder functor for semifree dg categories. This allows us to construct a homotopy colimit functor explicitly. These two functors are "computable", specifically, the constructed cylinder functor sends a dg category of finite type, i.e., a semifree dg category having finitely many generating morphisms, to a dg category of finite type. The homotopy colimit functor has a similar property. Moreover, using the cylinder functor, we give a cofibration category of semifree dg categories and that of dg categories of finite type, independently from the work of Tabuada. All the results similarly work for semifree dg algebras. We also describe an application to symplectic topology and provide a toy example. |
| title | A Computational Approach to the Homotopy Theory of DG categories |
| topic | Category Theory K-Theory and Homology Symplectic Geometry 18G35, 18N40, 18N45, 53D37 |
| url | https://arxiv.org/abs/2405.03258 |