Let $k$ be a commutative ring. Let $Ch(k)$ denote the monoidal category of chain complexes. I need a reference, including a proof, for the following "folklore fact" (see for example [here](https://arxiv.org/abs/0807.1471v1) after Definition 1.2.1):



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> A chain complex $A \in Ch(k)$ is dualizable if and only if it is bounded and each $A\_n$ is a dualizable, i.e. finitely generated projective $k$-module.
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The dual is then $(A^\*)\_n = (A\_{-n})^\*$.



Reference for dualizable chain complexes
This is Proposition 1.6 of 'Duality, Trace and Transfer' by Dold and Puppe, <http://www.maths.ed.ac.uk/~aar/papers/doldpup2.pdf>. 


