  We introduce all six operations for D-cap-modules on smooth rigid analytic
spaces by considering the derived category of complete bornological
D-cap-modules. We then focus on a full subcategory which should be thought of
as consisting of complexes with coadmissible cohomology, and establish
analogues of some classical results: Kashiwara's equivalence, stability of
coadmissibility under extraordinary inverse image for smooth morphisms and
direct image for projective morphisms, as well as the computation of relative
de Rham cohomology.
