  This paper addresses the question of how categorical symmetries act on
extended operators in quantum field theory. Building on recent results in two
dimensions, we introduce higher tube categories and algebras associated to
higher fusion category symmetries. We show that twisted sector extended
operators transform in higher representations of higher tube algebras and
interpret this result from the perspective of the sandwich construction of
finite symmetries via the Drinfeld center. Focusing on three dimensions, we
discuss a variety of examples to illustrate the general constructions. In the
case of invertible symmetries, we show that higher tube algebras are higher
analogues of twisted Drinfeld doubles of finite groups, generalising known
constructions in two dimensions. Building on this foundation, we discuss
non-invertible Ising-like symmetry categories obtained by gauging finite
subgroups. We also consider non-invertible topological symmetry lines described
by braided fusion categories and discuss connections to the M\"uger center and
braided module categories.
