2016 Fiscal Year Final Research Report
Category theory appearing in algebra and its applications
| Project/Area Number |
25800022
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kagoshima University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Keywords | 三角圏 / 完全圏 / biset関手 / Mackey関手 / Burnside環 |
|---|
| Outline of Final Research Achievements |
(1)Twin cotorsion pair on a triangulated category gives a simultaneous generalization of t-structure, cluster tilting subcategory and functorially finite rigid subcategory. We have given a condition for the heart of twin cotorsion pairs to be equivalent, by means of the associated functors.
(2)We have calculated the prime spectrum of the Burnside Tambara functor for a special kind of groups, and related it to the spectrum of the Burnside ring itself. We have also given a biset deformation of Tambara functors, which was known to Mackey functors.
We have shown that biset functors can be realized as a special kind of Mackey functors on a 2-category. Based on this result, describing the properties of multiplicative transfers of Burnside rings, we have revealed their 'partial Tambara' property。Besides, via the 2-category of finite groupoids, we have given a method to obtain a biset functor from a derivator on this 2-category.
|
| Free Research Field |
代数学における圏論
|
