  We establish a duality between flat affine group schemes and rigid tensor
categories equipped with a neutral fiber functor (called Tannakian lattice),
both defined over a Dedekind ring. We use this duality and the known Tannakian
duality due to Saavedra to study morphisms between flat affine group schemes.
Next, we apply our new duality to the category of stratified sheaves on a
smooth scheme over a Dedekind ring R to define the relative differential
fundamental group scheme of the given scheme and compare the fibers of this
group scheme with the fundamental group scheme of the fibers. When R is a
complete DVR of equal characteristic we show that this category is Tannakian in
the sense of Saavedra.
