# Cofibrancy of simplicial objects [duplicate]

Let $\mathcal{C}$ be a site. Consider $sPsh(\mathcal{C})$ be the equipped with the local projective model structure. Let $C_{\bullet}$ be a cofibrant object in $\mathcal{C}$ and let $y(C_\bullet)$ be its image via the Yoneda embedding. Is it true that $y(C_\bullet)$ is a cofibrant object in the local projective model structure? I am particularly interested when $\mathcal{C}=Diff$, and the localization is along the Cech covers.

The point is that it seems to me a folk statement that each simplicial presheaf which is a coproduct of representables is cofibrant. But I don't know any reference for that!!! The only results that I know is the one of Dugger

http://ncatlab.org/nlab/show/model+structure+on+simplicial+presheaves#CofibrantObjects

where there are some free-degenerancies conditions. So what about simplicial manifolds?