  The holographic principle, being a generic feature of quantum gravity, should
allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT
correspondence, in which the dual field theory has local conformal symmetry and
is defined on a manifold with boundary, is one such example. Inspired by the
quotienting of AdS$_3$ by spacetime isometries in order to construct
multiboundary wormholes dual to multipartite CFT$_2$ states, we find that this
correspondence can be understood by combining AdS/CFT with some appropriate
quotient procedure. Furthermore, in three bulk dimensions, we find example
quotient spaces of AdS$_3$ in order to construct "natural" bulk duals for
specific BCFT$_2$ vacuum states, one of which appears to describe a novel,
time-dependent BCFT$_2$ solution. We call this particular refinement of
AdS/BCFT, in which we use quotients, the quotient-AdS/BCFT correspondence.
