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We generalise two facts about finite dimensional algebras to finitedimensional differential graded algebras. The first is the Nakayama Lemma andthe second is that the simples can detect finite projective dimension. We provetwo dual versions which relate to Gorenstein differential graded algebras andKoszul duality respectively. As an application, we prove a corepresentabilityresult for finite dimensional differential graded algebras.

Reflecting Perfection for Finite Dimensional Differential Graded Algebras