Integrability in 2d CFT and line defects

One way to describe integrability of a two-dimensional field theory is to find an infinite system of commuting conserved charges. Starting from a 2d CFT with topological line defects, I will explain a simple condition which exhibits deformations of the CFT as integrable, provided one can simultaneously deforming the topological line defects in a coherent way. This condition has an algebraic counterpart: it can be understood as a Yetter-Drinfeld condition for modules over certain Hopf algebras.