  Symmetry topological field theory (SymTFT) is a very convenient tool to study
finite generalized symmetries of a given quantum field theory (QFT). In
particular, SymTFTs encode all the symmetry structures and properties including
anomalies. Recently this tool has been applied for non-finite symmetries as
well. In this paper, we take a different route, which consists of considering a
free theory rather than a topological field theory in the bulk. We call it
Symmetry Theory (SymTh). We study its topological operators together with the
free boundary conditions. We also propose a procedure that is analogous to the
sandwich construction of symmetry TFTs and it allows us to obtain the physical
QFT. We apply this to many examples, ranging from abelian $p$-form symmetries
to 2-groups, and the (solvable) case of group-like symmetries in quantum
mechanics. Finally, we provide a derivation for the SymTh of $\mathbb Q/
\mathbb Z$ non-invertible symmetries from the dimensional reduction of IIB
supergravity on the conifold. In addition, we give an ultraviolet (UV)
interpretation of the quantum Hall states dressing the non-invertible $\mathbb
Q/ \mathbb Z$ topological operators, in terms of branes in the IIB supergravity
background.
