  We extend the range of $N$ to negative values in the $(K,N)$-convexity (in
the sense of Erbar--Kuwada--Sturm), the weighted Ricci curvature $Ric_N$ and
the curvature-dimension condition $CD(K,N)$. We generalize a number of results
in the case of $N>0$ to this setting, including Bochner's inequality, the
Brunn--Minkowski inequality and the equivalence between $Ric_N \ge K$ and
$CD(K,N)$. We also show an expansion bound for gradient flows of Lipschitz
$(K,N)$-convex functions.
