Abstract:
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).