  Topology is routinely used to understand the physics of electronic
insulators. However, for strongly interacting electronic matter, such as Mott
insulators, a comprehensive topological characterization is still lacking. When
their ground state only contains short range entanglement and does not break
symmetries spontaneously, they generically realize crystalline symmetry
protected topological phases (cFSPTs), supporting gapless modes at the
boundaries or at the lattice defects. Here, we provide an exhaustive
classification of cFSPTs in two-dimensions (2D) with $\mathrm{U}(1)$
charge-conservation and spinful time-reversal symmetries, namely those
generically are present in spin-orbit coupled insulators, for any of the 17
wallpaper groups. It has been shown that the classification of cFSPTs can be
understood from appropriate real-space decorations of lower-dimensional
subspaces, and we expose how these relate to the Wyckoff positions of the
lattice. We find that all nontrivial one-dimensional decorations require
electronic interactions. Furthermore, we provide model Hamiltonians for various
decorations, and discuss the signatures of cFSPTs. This classification paves
the way to further explore topological interacting insulators, providing the
backbone information in generic model systems and ultimately in experiments.
