Appears in collection : Algèbre, Géométrie et Physique : une conférence en l'honneur

I define and study Topological Quantum Field Theories (TQFTs) which describe the low-energy limit of gapped phases of gauge theories. These TQFTs generalize the Dijkgraaf-Witten TQFT and can be described on a lattice using discrete 1-form and 2-form gauge fields. The gauge group is replaced by a gauge 2-group (a 2-category with a single object and invertible 1-morphisms and 2-morphisms). It is proposed that 2-group TQFTs are associated with new types of symmetry-protected gapped phases of matter