  The combinatorial Ricci curvature of Forman, which is defined at the edges of
a CW complex, and which makes use of only the face relations of the cells in
the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does
not behave analogously to smooth surfaces with respect to negative curvature.
We extend this curvature to vertices and faces in such a way that the problems
with combinatorial Ricci curvature are mostly resolved. The discussion is
stated in terms of ranked posets.
