Description
Any (n-pivotal) n-category C can be embedded in a Morita-equivalent completion C^#. Because of the Morita equivalence, any module/action of C automatically leads to one of the larger category C^#. In particular, discrete k-form symmetries of d-dimensional QFTs correspond to actions of C(G, d+1, k+1) = \pi_{\le d+1}(B^{k+1}(G)), and therefore give rise to actions of the completed (d+1)-category C(G, d+1, k+1)^#. While C(G, d+1, k+1) is built out of invertible morphisms, C(G, d+1, k+1)^# typically contains many non-invertible morphisms leading to non-invertible symmetries of the original QFT. I’ll also discuss how completed n-categories can be used to construct many new examples of Kramers-Wannier-type dualities. This is joint work with Fiona Burnell.
