Recall that any [extensive category](https://ncatlab.org/nlab/show/extensive+category) can be canonically endowed the structure of a site via the extensive topology, which is the Grothendieck topology whose covering morphisms are the coproduct injections.


I've heard that ($Cat$-valued) stacks for the extensive topology on an extensive category $C$ are precisely the pseudofunctors which send coproducts in $C$ to products in $Cat$. Is there an explicit proof of this anywhere?



Stacks for the extensive topology?
This a genral fact: the coproducts in an extensive category are disjoint so the sheaf/stack condition with respect to a cover by the coproduct injection exactly say that the coproduct is sent to a product. So if they are the only cover a sheaf or a stack is just a functor sending the coproduct to products.


