  We explain our previous results about Hochschild actions [Kau07a, Kau08a]
pertaining in particular to the coproduct which appeared in a different form in
[GH09] and provide a fresh look at the results. We recall the general action,
specialize to the aforementioned coproduct and prove that the assumption of
commutativity, made for convenience in [Kau08a], is not needed. We give
detailed background material on loop spaces, Hochschild complexes and
dualizations, and discuss details and extensions of these techniques which work
for all operations of [Kau07a, Kau08a].
  With respect to loop spaces, we show that the co--product is well defined
modulo constant loops and going one step further that in the case of a graded
Gorenstein Frobenius algebra, the co--product is well defined on the reduced
normalized Hochschild complex.
  We discuss several other aspects such as ``time reversal'' duality and
several homotopies of operations induced by it. This provides a cohomology
operation which is a homotopy of the anti--symmetrization of the coproduct. The
obstruction again vanishes on the reduced normalized Hochschild complex if the
Frobenius algebra is graded Gorenstein.
  Further structures such as ``animation'' and the BV structure and a coloring
for operations on chains and cochains and a Gerstenhaber double bracket are
briefly treated.
