  The Resolution Theorem for Compact Abelian Groups is applied to show that the
profinite subgroups of a finite-dimensional compact connected abelian group
(protorus) which induce tori quotients comprise a lattice under intersection
(meet) and $+$ (join), facilitating a proof of the existence of a universal
resolution. A finite rank torsion-free abelian group $X$ is algebraically
isomorphic to a canonical dense subgroup $X_G$ of its Pontryagin dual $G$. A
morphism between protori lifts to a product morphism between the universal
covers, so morphisms in the category can be studied as pairs of maps:
homomorphisms between finitely generated profinite abelian groups and linear
maps between finite-dimensional real vector spaces. A concept of
non-Archimedean dimension is introduced which acts a useful invariant for
classifying protori.
