Applied Categorical Structures

, Volume 19, Issue 6, pp 879–899

General Heart Construction on a Triangulated Category (I): Unifying t-Structures and Cluster Tilting Subcategories

Article

DOI: 10.1007/s10485-010-9223-2

Cite this article as:
Nakaoka, H. Appl Categor Struct (2011) 19: 879. doi:10.1007/s10485-010-9223-2

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.

Keywords

Triangulated categoryt-structureCluster tilting subcategoryHeart

Mathematics Subject Classification (2000)

18E30

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan