  To any model category $\mathcal{M}$, we associate a modular model category, a
functor of points $\mathcal{M}[-]:$ Cat $\rightarrow$ Cat, that associates to
any small category $\mathcal{C}$ a functor category $\mathcal{M}[\mathcal{C}] =
\text{Fun}_{fes}(\mathcal{C}, \mathcal{M})$ of full and essentially surjective
functors from $\mathcal{C}$ to $\mathcal{M}$, providing parametrizations of a
same model category $\mathcal{M}$ by different small categories. We are in
particular interested in using schemes as parameters. We consider
$\mathbb{Z}$Sm$/k$ the category of linear combinations of smooth separated
schemes of finite type over Spec($k$), $k$ a field, referred to as
$\mathbb{Z}$-schemes, and let $\mathcal{C} = Sh(\mathbb{Z} \text{Sm}/k,
\text{Nis})$. We contrast this with using the $\mathbb{A}^1$-homotopy category
of $\mathbb{Z}$-schemes as a parametrizing category.
