We prove that there exists a class of crystalline insulators, which we call "weak Mott insulators", which are not adiabatically connected to any sort of band insulator provided time-reversal and certain point-group symmetries are respected, but which are otherwise unspectacular in that they exhibit no topological order nor any form of exotic quasi-particles. We illustrate this new type of insulators with two examples: the d-Mott insulator discovered in the checkerboard Hubbard model at half-filling and the AKLT insulator on the square lattice.