| Project/Area Number |
25610002
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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 | Shinshu University |
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Principal Investigator |
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| Research Collaborator |
MATSUO Kentaro
MOMOSE Yasuhiro
HANAKI Akihide 信州大学, 学術研究院理学系, 教授 (50262647)
NUMATA Yasuhide 信州大学, 学術研究院理学系, 准教授 (00455685)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | スキーモイド / 2-圏 / 森田同値 / 強ホモトピー / モデル圏 / Mitchell埋め込み定理 / アソシエーションスキーム / 小圏のコホモロジー / 関手圏 / 小圏 / コホモロジー |
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| Outline of Final Research Achievements |
We have proposed the notion of (association) schemoids generalizing that of association schemes, which are widely used in algebraic combinatorics, from a small categorical point of view. In our study, the equivalence between the categories of groupoids and that of thin schemoids is established. Moreover, in order to develop homotopy theory for schemoids, we define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. In consequence, the 2-category of small categories is embedded into the 2-category of quasi-schemoids. As for categorical representation theory for schemoids, we have proved Mitchell's embedding theorem for a tame schemoid. The result allows us to give a cofibrantly generated model category structure to the category of chain complexes over a functor category with a schemoid as the domain. We show that every Hamming scheme of binary codes is Morita equivalent to the association scheme arising from the cyclic group of order two.
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