Non-Invertible Symmetries

Symmetries of Quantum Field Theories (QFTs), whose fusion does not satisfy a group multiplication law, are generally referred to as non-invertible. I will discuss their connection to generalized gauging and higher fusion categories, providing by concrete examples in 3d and 4d QFTs. Complementing the field theoretic approach, I will discuss how non-invertible symmetries are realized in holographic dualities, and explain how branes realize the symmetry generators in these setups.