| Project/Area Number |
21540036
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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) |
YAMAGATA Kunio 東京農工大学, 工学研究院, 教授 (60015849)
MORI Izuru 静岡大学, 理学部, 准教授 (50436903)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 多元環 / 導来圏 / グロタンディーク構成 / 被覆 / ラックス関手 / ホール代数 / 導来同値 / 2圏 / 反復圏 / 軌道圏 / スマッシュ積 / 群作用 / 次数付き圏 |
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| Research Abstract |
Let k be a commutative ring, I a small category and denote by k-Cat the 2-category of small k-categories. For 2-categories B, C, denote by Colax(B,C) the 2-category consisting of the colax functors from B to C and the lax transformations between them. We proved that each pseudofuncor C→D of 2-categories induces a pseudofunctor Colax(B,C)→Colax(B,D) for all 2-categories B, and defined the "module category", the "derived category", and derived equivalences of colax functors I→k-Cat by using it. We proved that if two such colax functors are derived equivalent, then so are their Grothendieck constructions, by which we gave a way to glue derived equivalences together.
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