名古屋大学 · 数学
中岡弘之教授の研究室は、加群圏や三角圏の一般化として導入された「外部加群圏（extriangulated categories）」を軸に、コトルシオン対やモデル構造、ホモトピー圏の構造に関する理論を発展させています。特に、Hoveyの双対コトルシオン対と適切なモデル構造の対応関係を解明し、局所化とイデアル商の関係をホモトピー圏を通じて統一的に扱う枠組みを構築しています。また、Iyama–Yoshinoの還元やrecollementの一般化としての「同心双対コトルシオン対」の導入により、コトルシオン対の一般化された変形（ミューテーション）の理論を展開しています。
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We give a simultaneous generalization of exact categories and triangulated\ncategories, which is suitable for considering cotorsion pairs, and which we\ncall extriangulated categories. Extension-closed, full subcategories of\ntriangulated categories are examples of extriangulated categories. We give a\nbijective correspondence between some pairs of cotorsion pairs which we call\nHovey twin cotorsion pairs, and admissible model structures. As a consequence,\nthese model structures relate certain
We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories. Extension-closed, full subcategories of triangulated categories are examples of extriangulated categories. We give a bijective correspondence between some pairs of cotorsion pairs which we call Hovey twin cotorsion pairs, and admissible model structures. As a consequence, these model structures relate certain locali
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a natural extriangulated structure.
In this article, we investigate the condition for the hearts of twin cotorsion pairs to be equivalent, compatibly with the associated functors. This is related to the vanishing of components of pairs through the associated functors.
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