Are Generalised Symmetries Symmetries?

Traditionally, a symmetry of a quantum system refers to a transformation that preserves transition probabilities between physical states. In recent years, this notion has been expanded to so-called generalised symmetries, which correspond to (possibly non-invertible) topological defects in quantum field theory. At first sight, it is not obvious how the above two notions of symmetry are related. In this talk, I will review the notion of generalised symmetries and discuss how they relate to (and depart from) the traditional notion of symmetry.