The Stacks project

113.4 Stacks

We have a chapter on (abstract) stacks, see Stacks, Section 8.1. It would be nice if

1. improve the discussion on “stackyfication”,

2. give examples of stackyfication,

3. more examples in general,

4. improve the discussion of gerbes.

Example result which has not been added yet: Given a sheaf of abelian groups $\mathcal{F}$ over $\mathcal{C}$ the set of equivalence classes of gerbes banded by $\mathcal{F}$ is bijective to $H^2(\mathcal{C}, \mathcal{F})$.