Nagoya University · Mathematics
Professor Hiroyuki Nakaoka's research lab specializes in advanced homological algebra and category theory, focusing on extriangulated categories as a unifying framework that generalizes both exact and triangulated categories. The lab investigates cotorsion pairs, Hovey twin cotorsion pairs, and their connections to model structures, homotopy categories, and recollements in triangulated settings. A central theme is the development of generalized reduction and mutation operations for cotorsion pairs, particularly through the concept of concentric twin cotorsion pairs, which unify t-structures, cluster tilting, and co-t-structures. The lab also explores applications in algebraic topology and representation theory, including Tambara functors and their role in Witt–Burnside constructions.
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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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