  We define a dg-category of looped diagrams which we use to construct
operations on the Hochschild complex of commutative Frobenius dg-algebras. We
show that we recover the operations known for symmetric Frobenius dg-algebras
constructed using Sullivan chord diagrams as well as all formal operations for
commutative algebras (including Loday's lambda operations) and prove that there
is a chain level version of a suspended Cactus operad inside the complex of
looped diagrams. This recovers the suspended BV algebra structure on the
Hochschild homology of commutative Frobenius algebras defined by Abbaspour and
proves that it comes from an action on the Hochschild chains.
