  The concept of Gromov hyperbolicity manifests itself in many different ways.
With only mild assumptions on the underlying metric space, the spectrum of
equivalent properties includes various thin triangle conditions, the stability
of quasi-geodesics (the Morse lemma), a linear isoperimetric filling inequality
for closed curves, and a sub-quadratic isoperimetric inequality. We present a
similar list of six equivalent properties in the context of generalized
non-positive curvature and higher asymptotic rank. This complements results of
Wenger and of Kleiner and the second author. We give a largely self-contained
proof, providing some improvements and simplifications for the known part.
