In mathematics, the Schauenbug–Ng theorem is a theorem about the modular group representations of modular tensor categories proved by Siu-Hung Ng and Peter Schauenburg in 2010. It asserts that that the kernels of the modular representations of all modular tensor categories are congruence subgroups of . Since congruence subgroups all have finite index in , this implies in particular that the modular representations of all modular representations have finite image.