2015 Fiscal Year Final Research Report
2-categorical covering theory for algebras
| Project/Area Number |
25610003
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
IYAMA Osamu 名古屋大学, 大学院多元数理科学研究科, 教授 (70347532)
TAMAKI Dai 信州大学, 理学部, 教授 (10252058)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 被覆 / グロタンディーク構成 / スマッシュ積 / 導来同値 / 2圏 / 軌道圏 / 両側加群 |
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| Outline of Final Research Achievements |
We fix a commutative ring k, a small k-category I and a group G. 1. We denote by k-Catb the bicategory of all small k-categories with bimodules over them as 1-morphisms. We gave a natural definitions of "module category" Mod X and "derived category" D(Mod X) of a lax functor X:I-> Catb as lax functors, and defined a notion of derived equivalences between lax functors X. We proved that if lax functors X, X':I -> k-Catb are derived equivalent, then so are their Grothendieck constructions Gr(X) and Gr(X'). 2. We established a covering theory for bimodules over small k-categories. 3. For G-graded small k-categories R and S that are derived equivalent, we gave a sufficient condition for the smash products R#G and S#G to be derived equivalent.
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| Free Research Field |
数学
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