An algebra whose syzygy-intersection category has only finitely many indecomposables is left weakly Gorenstein; this covers monomial algebras and endomorphism rings of modules over representation-finite algebras.
Contemporary Mathematics Volume 406, 2006
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On weakly Gorenstein algebras
An algebra whose syzygy-intersection category has only finitely many indecomposables is left weakly Gorenstein; this covers monomial algebras and endomorphism rings of modules over representation-finite algebras.