Prestacks do not arise often in nature so people do not write about their properties, sadly I found one in the wild.
I've tried finding a reference which proves basic properties of prestacks, but all I can find are properties of stacks and a definition of prestacks. Ideally I would like a natural reference to cite. I've tried to find mention in the stacks project and failed [perhaps I am incompetent?] as this would be the best thing to cite.
The results I am interested in are:
- Does the category of prestacks admit colimits? (I could probably prove this, but it is more natural to cite).
- If I construct a morphism from a prestack F to a stack F' and show it is an isomorphism on stalks then does the stackification of F coincide with F'. (I expect something along the lines of "stacks are local" to be true. I could probably prove the right statement with enough time but once again it would be more natural to cite).