  In this paper, we study conditions for extending Quillen model category
properties , between two symmetric monoidal categories, to their associated
category of symmetric sequences and of operads.
  Given a Quillen equivalence $\lambda: \mathcal{C}=Ch_{\Bbbk,t}
\leftrightarrows \mathcal{D}: R,$ so that $\mathcal{D}$ is any symmetric
monoidal category and the adjoint pair $(\lambda, R)$ is weak monoidal, we
prove that the categories of connected operads $Op_\mathcal{C}$ and
$Op_\mathcal{D}$ are Quillen equivalent. This expands an analogous result of
Schwede-Shipley(\cite{SS03}) when we replace these categories of operads with
the sub-categories of $\mathcal{C}$-Monoid and $\mathcal{D}$-monoid.
