  We study the structure of Gromov-Hausdorff limits of sequences of Riemannian
manifolds $\{(M_\alpha^n,g_\alpha)\}_{\alpha \in A}$ whose Ricci curvature
satisfies a uniform Kato bound. We first obtain Mosco convergence of the
Dirichlet energies to the Cheeger energy and show that tangent cones of such
limits satisfy the $\mathrm{RCD}(0,n)$ condition. When assuming a
non-collapsing assumption, we introduce a new family of monotone quantities,
which allows us to prove that tangent cones are also metric cones. We then show
the existence of a well-defined stratification in terms of splittings of
tangent cones. We finally prove volume convergence to the Hausdorff
$n$-measure.
