Abstract
In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394, 245–284 (2013)”, we introduced the notion of the heart for any cotorsion pair on an exact category with enough projectives and injectives, and showed that it is an abelian category. In this paper, we construct a half exact functor from the exact category to the heart. This is an analog of the construction of Abe and Nakaoka for triangulated categories. We will also use this half exact functor to find out a sufficient condition when two different hearts are equivalent.
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The author would like to thank Osamu Iyama for his helpful advices and corrections.
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Supported by Fundamental Research Funds for the Central Universities (Grant No. 2682018ZT25)
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Liu, Y. Half Exact Functors Associated with Cotorsion Pairs on Exact Categories. Acta. Math. Sin.-English Ser. 35, 1334–1356 (2019). https://doi.org/10.1007/s10114-019-8216-9
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DOI: https://doi.org/10.1007/s10114-019-8216-9