In the case of 1-categories, we know there is a functor category 
$PSh(C):=[C^{op},Set]$, where $C$ is a small category,
and this functor category is a topos. I am hoping this will extend to the case of 2-categories and especially the 2-category of groupoids.



Does the 1-category construction of a topos of presheaves extend to the 2-Category of Groupoids?
Gpd is the 2-category of groupoidd.


The category of 2-functors and natural transformations $Gpd^{op} \rightarrow C$, for $C$ any 1-category is equivalent to the category $Gpd'^{op} \rightarrow C$ of functors and natural transformations, where $Gpd'$ has the same objects as $Gpd$ but isomorphism classes of functors as arrows. The category $[Gpd'^{op},Set]$ is a presheaf topos.


