  Let X be a smooth variety over a perfect field of characteristic p>0. In this
small note we define overconvergent F-de Rham-Witt connections as an analogue
for F-crystals over proper schemes. We prove that the forgetful functor from
the category of overconvergent F-de Rham-Witt connections to the category of
convergent F-de Rham-Witt connections is fully faithful. The argument is an
analogue of a discussion by Kedlaya on full faithfulness of overconvergent
F-isocrystals.}
