Let $\mathcal C$ be a small category, the category of simplicial presheaf $sPre$ over $\mathcal C$ is the functor category $\mathcal C^{op} \rightarrow sSet$. Or equivalently simplicial objects in $\mathcal C^{op}\rightarrow Set$.
In Jardine's book local homotopy theory P.106, above the corollary 5.19, he assert that every simplicial presheaf $X$ is a colimit of objects $U\times \Delta^n$. Where $U$ is identified with $\hom_{\mathcal C}(-, U)$, and $\Delta^n$ is the standard simplicial set.
There is a funtion complex $\hom(X,Y)$ for simplicial presheaves $X,Y$, defined by $\hom(X,Y)_n=\hom_{sPre}(X\times\Delta^n,Y)$, one can show that we have the following isomorphism $$\hom(\hom_{\mathcal C}(-, U), X)\cong X(U).$$ Since every simplicial set is colimit of representable functor, we have $X(U)\cong \varinjlim\Delta^n,$
I don't know how to show that $X$ is a colimit of $U\times\Delta^n$. Any suggestions?