  The purpose of this paper is twofold. First, we review applications of the
bar duality of operads to the construction of explicit cofibrant replacements
in categories of algebras over an operad. In view toward applications, we check
that the constructions of the bar duality work properly for algebras over
operads in unbounded differential graded modules over a ring.
  In a second part, we use the operadic cobar construction to define explicit
cyclinder objects in the category of operads. Then we apply this construction
to prove that certain homotopy morphisms of algebras over operads are
equivalent to left homotopies in the model category of operads.
