Abstract
The aim of this paper is to introduce the concept of right and left semidualizing adjoint pair of functors and study its main properties. This concept generalizes the concept of semidualizing module and allows one to consider semidualizing comodules, graded modules, etc. We also study tilting adjoint pair of functors as a particular case. We show generalized tilting theorem in this general setting and give some applications to tilting theory in the category of comodules over a coalgebra.
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Acknowledgments
First and third authors are supported by the Grants MTM2011-27090 from Ministerio de Ciencia e Innovación FEDER and P07-FQM-0312 from Junta de Andalucía. The second author is supported by DGES BFM2002-02717 Grant and Junta de Andalucía FQM 0211. We thank the referee for pointing out the article [35] and for his/her helpful suggestions for improving the paper.
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Communicated by Jie Du.
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Rozas, J.R.G., Ramos, J.A.L. & Torrecillas, B. Semidualizing and Tilting Adjoint Pairs, Applications to Comodules. Bull. Malays. Math. Sci. Soc. 38, 197–218 (2015). https://doi.org/10.1007/s40840-014-0013-0
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DOI: https://doi.org/10.1007/s40840-014-0013-0