## “School of Mathematics”

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Paper   IPM / M / 17002
School of Mathematics
Title:   A functional approach to categorical resolutions
Author(s):
 1 Rasool Hafezi 2 Mohammad Hossein Keshavarz
Status:   Published
Journal: Science China Mathematics
Vol.:  63
Year:  2020
Pages:   1-12
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.