  We introduce global model categories as a general framework to capture
several phenomena in global equivariant homotopy theory. We then construct
genuine stabilizations of these, generalizing the usual passage from unstable
to stable global homotopy theory. Finally, we define the global topological
Andr\'e-Quillen cohomology of an ultra-commutative ring spectrum and express it
in terms of a genuine stabilization in our framework in analogy with the
classical non-equivariant description obtained by Basterra and Mandell.
