  Orbifold singularities of M-theory constitute the building blocks of a broad
class of supersymmetric quantum field theories (SQFTs). In this paper we show
how the local data of these geometries determines global data on the resulting
higher symmetries of these systems. In particular, via a process of cutting and
gluing, we show how local orbifold singularities encode the 0-form, 1-form and
2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from
the possible singularities which extend to the boundary of the non-compact
geometry. The resulting category of boundary conditions then captures these
symmetries, and is equivalently specified by the orbifold homology of the
boundary geometry. We illustrate these general points in the context of a
number of examples, including 5D superconformal field theories engineered via
orbifold singularities, 5D gauge theories engineered via singular elliptically
fibered Calabi-Yau threefolds, as well as 4D SQCD-like theories engineered via
M-theory on non-compact $G_2$ spaces.
