  We study the anomalies of non-invertible symmetries in 1+1D QFTs using gapped
boundaries of its SymTFT. We establish the explicit relation between Lagrangian
algebras which determine gapped boundaries of the SymTFT, and algebras which
determine non-anomalous/gaugeable topological line operators in the 1+1D QFT.
If the Lagrangian algebras in the SymTFT are known, this provides a method to
compute algebras in all fusion categories that share the same SymTFT. We find
necessary conditions that a line operator in the SymTFT must satisfy for the
corresponding line operator in the 1+1D QFT to be non-anomalous. We use this
constraint to show that a non-invertible symmetry admits a 1+1D trivially
gapped phase if and only if the SymTFT admits a magnetic Lagrangian algebra. We
define a process of transporting non-anomalous line operators between fusion
categories which share the same SymTFT and apply this method to the three
Haagerup fusion categories.
