Abstract
It is well known that the bar resolution can be replaced with any projective
resolution of the corresponding algebra when computing the Hochschild
(co)homology of that algebra. This is, in fact, a feature of its construction
via derived functors. For generalizations and extensions of the Hochschild
(co)homology, one uses a bar-like resolution in a simplicial setting in order
to accommodate the changing module structures in every dimension. In this note,
we present a method in order to replace these bar-like resolutions.