I will present a joint work with Gilles Carron and Ilaria Mondello where we provide a relationship between the Bakry-Émery curvature-dimension condition for weighted Riemannian manifolds and a Kato condition on the Ricci curvature for Riemannian manifolds. I will explain how this is done by means of a suitable time change, and how we deduce from this several improvements over our previous results on the structure of Kato limit spaces. The latter are Gromov-Hausdorff limits of Riemannian manifolds satisfying a uniform Kato condition on the Ricci curvature.