Abstract
Using a relative version of Auslander’s formula, we give a functorial approach to show that the bounded derived category of every Artin algebra admits a categorical resolution. This, in particular, implies that the bounded derived categories of Artin algebras of finite global dimension determine bounded derived categories of all Artin algebras. Hence, this paper can be considered as a typical application of functor categories, introduced in representation theory by Auslander (1971), to categorical resolutions.
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Acknowledgments
This work was supported by a grant from Institute for Research in Fundamental Sciences (IPM) (Grant No. 98130021). The authors thank the referees for carefully reading the manuscript and many helpful comment and hints that improved our exposition.
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Hafezi, R., Keshavarz, M.H. A functorial approach to categorical resolutions. Sci. China Math. 63, 2005–2016 (2020). https://doi.org/10.1007/s11425-018-1614-3
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DOI: https://doi.org/10.1007/s11425-018-1614-3