I will define a certain type of properadic algebra called a Y-infinity algebra, which is an A-infinity algebra together with higher structure maps encoding a certain type of Poincaré duality structure. In particular, the algebra of chains on the based loop space of any oriented manifold is canonically endowed with this type of structure. By using the formalism of properadic Kaledin classes, we can study these algebraic structures and detect their formality, or lack thereof. I will also explain the relation between these algebraic structures and string topology operations, and how Y-infinity formality plays a role in understanding these operations. This talk is about joint work C. Emprin.