Under cograde conditions, Tor-Ext and Ext-Tor double functors preserve morphisms, yielding two complete cotorsion pairs and a link between relative finitistic dimensions and projective dimensions of a semidualizing bimodule.
W akamatsu, Stable equivalence for self-injective algebras and a gener alization of tilt- ing modules , J
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Cograde conditions and cotorsion pairs
Under cograde conditions, Tor-Ext and Ext-Tor double functors preserve morphisms, yielding two complete cotorsion pairs and a link between relative finitistic dimensions and projective dimensions of a semidualizing bimodule.