  We study generalized symmetries in a simplified arena in which the usual
quantum field theories of physics are replaced with topological field theories
and the smooth structure with which the symmetry groups of physics are usually
endowed is forgotten. Doing so allows many questions of physical interest to be
answered using the tools of homotopy theory. We study both global and gauge
symmetries, as well as `t Hooft anomalies, which we show fall into one of two
classes. Our approach also allows some insight into earlier work on symmetries
(generalized or not) of topological field theories.
