# nLab 2-gerbe

### Context

#### Bundles

bundles

fiber bundles in physics

cohomology

# Contents

## Definition

### Nonabelian 2-gerbes

For $\mathcal{X}$ an (∞,1)-topos, a 2-gerbe $P$ in $\mathcal{X}$ is an object which is

The first condition says that it is an (∞,1)-sheaf with values in 2-groupoids. The second says that $P \to *$ is an effective epimorphism and that the 0-th homotopy sheaf is the terminal sheaf. In the literature this is often stated as saying that $P$ is a) locally connected and b) locally non-empty .

### Abelian 2-gerbes

For $\mathcal{X}$ an (∞,1)-topos, an abelian 2-gerbe $P$ in $\mathcal{X}$ is an object which is

## References

A comprehensive discussion of nonabelian 2-gerbes is in

• Lawrence Breen, On the classification of 2-gerbes and 2-stacks , Astérisque 225 (1994).

A more expository discussion is in

Abelian 2-gerbes are a special case (see ∞-gerbe) of the discussion in section 7.2.2 of