The dual of a complex $C$ is by definition $\operatorname{Hom}(C, R)$, where $R$ is the ring of $C$.
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The double dual is not necessarily isomorphic to the original complex.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Complexes/ChainComplexDoc.m2:2778:0.