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In the paper of Keller and Reiten, it was shown that the quotient of atriangulated category (with some conditions) by a cluster tilting subcategorybecomes an abelian category. After that, Koenig and Zhu showed in detail, howthe abelian structure is given on this quotient category, in a more abstractsetting. On the other hand, as is well known since 1980s, the heart of any$t$-structure is abelian. We unify these two construction by using the notionof a cotorsion pair. To any cotorsion pair in a triangulated category, we cannaturally associate an abelian category, which gives back each of the above twoabelian categories, when the cotorsion pair comes from a cluster tiltingsubcategory, or is a $t$-structure, respectively.

General heart construction on a triangulated category (I): unifying t-structures and cluster tilting subcategories