  Final coalgebras as "categorical greatest fixed points" play a central role
in the theory of coalgebras. Somewhat analogously, most proof methods studied
therein have focused on greatest fixed-point properties like safety and
bisimilarity. Here we make a step towards categorical proof methods for least
fixed-point properties over dynamical systems modeled as coalgebras.
Concretely, we seek a categorical axiomatization of well-known proof methods
for liveness, namely ranking functions (in nondeterministic settings) and
ranking supermartingales (in probabilistic ones). We find an answer in a
suitable combination of coalgebraic simulation (studied previously by the
authors) and corecursive algebra as a classifier for (non-)well-foundedness.
