Suppose $f:X\longrightarrow Y$ is a morphism of schemes. Take the categories $\mathbf{X}_{et},\,\mathbf{Y}_{et}$ of étale morphisms over $X$ and $Y$. Then is the direct image functor:
$f_{*}:\mathbf{PSh}(\mathbf{X}_{et})\longrightarrow\mathbf{PSh}(\mathbf{Y}_{et})$
on category of presheaves exact? I know it's left-exact if restricted to the category of sheaves on étale site, but what does exactness mean in the category of presheaves on a site?