  We prove generalized lower Ricci curvature bounds for warped products over
complete Finsler manifolds. On the one hand our result covers a theorem of
Bacher and Sturm concerning euclidean and spherical cones. On the other hand it
can be seen in analogy to a result of Bishop and Alexander in the setting of
Alexandrov spaces with curvature bounded from below. For the proof we combine
techniques developed in these papers. Because the Finsler product metric can
degenerate we regard a warped product as metric measure space that is in
general neither a Finsler manifold nor an Alexandrov space again but a space
satisfying a curvature-dimension condition in the sense of Lott-Villani/Sturm.
