We now come to the notion of a variety with respect to a localization datum. A variety is an object $X$ of $\Sh{M}$ that is covered by affine varieties that are étalé over $X$. The advantage of varieties in comparison to other objects of $\Sh{M}$ is: if $X$ is a variety, let $\ET/X$ be the full subcategory of $M/X$ spanned by affine étalés over $X$. $\Sh{\ET/X}$ is the topos of étale’s over $X$ (we may remark that if $Y$ is étalé over a variety $X$, then $Y$ is also a variety). We have the same functors $\Sum{i}$, $i^\sharp$, and $\Prod{i}$ between the little topos $\Sh{\ET/X}$ and the big topos $\Sh{M}/X$.