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smooth algebra
A definition due to Kontsevich: a DGA \(A\) is smooth if \(A \in \mathsf{Perf}\left(A \otimes A^{^{\operatorname{op}}} \right)\). It is compact if \(\operatorname{dim} H^{\bullet}(A, d)<\infty\). This properties are preserved under the derived Morita equivalence.
