<p>This report proposes the novel relation between gravity and the weak force, namely the graviweak correspondence. We construct a geometrical Yang-Mills theory that includes gravity, called the Yang-Mills-Utiyama theory. The theory treats the space-time symmetry of the local Lorentz group in the same manner as the internal gauge symmetry. We extend the theory into a more expansive space, including Euclidean and Lorentzian metrics at its boundaries. This extension suggests a relation between space-time and internal symmetry. The perspective provided by the extended theory suggests the novel relation between gravity and the weak force, leading us to the graviweak correspondence.</p>