General Heart Construction on a Triangulated Category (I): Unifying <Emphasis Type="Italic">t</Emphasis>-Structures and Cluster Tilting Subcategories |
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Authors: | Hiroyuki Nakaoka |
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Institution: | 1.Graduate School of Mathematical Sciences,The University of Tokyo,Tokyo,Japan |
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Abstract: | In the paper of Keller and Reiten, it was shown that the quotient of a triangulated category (with some conditions) by a cluster
tilting subcategory becomes an abelian category. After that, Koenig and Zhu showed in detail, how the abelian structure is
given on this quotient category, in a more abstract setting. On the other hand, as is well known since 1980s, the heart of
any t-structure is abelian. We unify these two constructions by using the notion of a cotorsion pair. To any cotorsion pair in
a triangulated category, we can naturally associate an abelian category, which gives back each of the above two abelian categories,
when the cotorsion pair comes from a cluster tilting subcategory, or a t-structure, respectively. |
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Keywords: | |
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