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## “School of Mathematics”

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Paper   IPM / M / 16035
School of Mathematics
Title:   A functorial approach to categorical resolutions
Author(s):
 1 . Rasool Hafezi 2 . Mohammad Hossein Keshavarz
Status:   Publishied
Journal: Science China Mathematics
Year:  2020
Pages:   DOI: 10.1007/s11425-018-1614-3
Supported by:  IPM
Abstract:
Using a relative version of Auslanderâ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.