Special precovered categories of Gorenstein categories

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Abstract

Let A be an abelian category and P(A) be the subcategory of A consisting of projective objects. Let C be a full, additive and self-orthogonal subcategory of A with P(A) a generator, and let G(C) be the Gorenstein subcategory of A. Then the right 1-orthogonal category \(G{(L)^{{ \bot _1}}}\) of G(C) is both projectively resolving and injectively coresolving in A. We also get that the subcategory SPC(G(C)) of A consisting of objects admitting special G(C)-precovers is closed under extensions and C-stable direct summands (*). Furthermore, if C is a generator for \(G{(L)^{{ \bot _1}}}\), then we have that SPC(G(C)) is the minimal subcategory of A containing \(G{(L)^{{ \bot _1}}}\)G(C) with respect to the property (*), and that SPC(G(C)) is C-resolving in A with a C-proper generator C.

Keywords

Gorenstein categories right 1-orthogonal categories special precovers special precovered cate- gories projectively resolving injectively coresolving 

MSC(2010)

18G25 18E10 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11571164), a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, the University Postgraduate Research and Innovation Project of Jiangsu Province 2016 (Grant No. KYZZ16 0034), Nanjing University Innovation and Creative Program for PhD Candidate (Grant No. 2016011). The authors thank the referees for the useful suggestions.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina

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