  Gauging is a general procedure for mapping a quantum many-body system with a
global symmetry to one with a local gauge symmetry. We consider a generalized
gauging map that does not enforce gauge symmetry at all lattice sites, and show
that it is an isometry on the full input space including all charged sectors.
We apply this generalized gauging map to convert global-symmetric bulk systems
of holographic codes to gauge-symmetric bulk systems, and vice versa, while
preserving duality with a global-symmetric boundary. We separately construct
holographic codes with gauge-symmetric bulk systems by directly imposing
gauge-invariance constraints onto existing holographic codes, and show that the
resulting bulk gauge symmetries are dual to boundary global symmetries.
Combining these ideas produces a toy model that captures several interesting
features of holography - it exhibits a rudimentary sort of dynamical duality,
can be modified to demonstrate the relationship between metric fluctuations and
approximate error-correction, and serves as an illustration for certain no-go
theorems concerning symmetries in holography. Finally, we apply the generalized
gauging map to construct codes with arbitrary transversal gate sets - for any
compact Lie group, we use a symmetry-preserving truncation scheme to construct
covariant finite-dimensional approximate holographic codes.
