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In the papers of Nakaoka, he introduced the notion of hearts of (twin)cotorsion pairs on triangulated categories and showed that they have structuresof (semi-) abelian categories. We study in this article a twin cotorsion pair(S,T),(U,V) on an exact category B with enough projectives and injectives andintroduce a notion of the heart. First we show that its heart is preabelian.Moreover we show the heart of a single cotorsion pair is abelian. These resultsare analog of Nakaoka's results in triangulated categories. We also considerspecial cases where the heart has nicer structure. By our results, the heart ofa special twin cotorsion pair (S,T),(T,V), is integral and almost abelian.Finally we show that the Gabriel-Zisman localisation of the heart at the classof regular morphisms is abelian, and moreover it is equivalent to the categoryof finitely presented modules over a stable subcategory of B.

Hearts of twin cotorsion pairs on exact categories