Nuclear modules over proper DG algebras

I will explain a certain construction of a dualizable presentable DG category Nuc(A) of "nuclear modules" over a proper DG algebra A. As a special case this construction gives the category of nuclear modules on an affine formal scheme (more precisely, its "unbounded" version), which was defined recently by Clausen and Scholze. For a smooth and proper DG algebra A the category Nuc(A) is equivalent to the usual category of A-modules.
I will also explain that this construction is a special case of internal Hom in an appropriate symmetric monoidal category (where the objects are dualizable presentable DG categories, and the morphisms are strongly continuous functors).