# Questions tagged [gerbes]

"Gerbe" is a construct in homological algebra and topology. They can be seen as a generalization of principal bundles to the setting of 2-categories. "Gerbe" is a French (and archaic English) word that literally means wheat sheaf. Gerbes were introduced by Jean Giraud (Giraud 1971) following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2.

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### Confusion in understanding the notion of $G$ Principal bundle where $G$ is a geometric group over a site

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### What is the geometric description of the set of isomorphism class of $G$-torsors over a site $C$?

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### Kottwitz global gerbes

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### How should one think about the band of a gerbe?

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### Lie groupoid $G$ extensions and principal $\text{Out}(G)$ bundles over Lie groupoids

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### Weak 2-groups and non-abelian gerbe over a manifold

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### Geometric models for 2-gerbes

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### Prerequisites for understanding algebraic geometry of “algebraic gerbes”

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### Concerning the definition of a 2-crossed module

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### Roadmap to understand gerbe in the sense of Lurie’s Higher Topos Theory

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### Central extension gives a gerbe over stack

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### Understanding the definition of $G$-gerbe

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### Examples of of gerbe over stacks in terms of manifolds

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### “Gerbes” in the cobordism theory

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### Is a gerbe over a manifold is a special case of a gerbe over a stack?

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### Understanding definition of gerbe over a stack

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### Cohomological description of gerbes over stacks

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### Cocycle description of gerbes

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### Crossed modules in context of gerbes

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### holonomy of connection on gerbes

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### Confusion in definition of Gerbes in Hitchin's notes

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### Connection on a Principal bundle and transition functions, as in Hitchin's notes

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### Trivializations of gerbes as generalisation of trivializations of line bundles

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### References on Gerbes

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### What is there in the book Cohomologie non abélienne by Jean Giraud

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### What is an example of a non-abelian gerbe with connection?

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### Categorical formalism for higher non-abelian group cohomology / obstruction theory for gerbes?

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### Sections of gerbes that can “vanish”

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### Residual gerbe and field of moduli

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### On $G$-gerbes over the punctured disk

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### Phenomena of gerbes

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### Gerbes on the multiplicative group

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### Smooth algebraic stacks with precisely two $\mathbb C$-objects

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### Fiberwise criterion for a stack to be a gerbe

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### Are there any non-trivial $G$-gerbes over the analytic space $\mathbb C$

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### Writing down gerbes explicitly over the projective line

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### Gerbes and Stacks

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### Connection on 3-bundle given as triplet of forms

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### Where are there defined objects between gerbes and bundle gerbes?

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### Gabber's proof of Br' = Br for quasiprojective schemes

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### Are deformations of a scheme some kind of a “derived gerbe” under the cotangent complex?

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### Differential Geometry of (Non-Abelian) Gerbes in the language of Brylinski

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### Second nonabelian group cohomology: cocycles vs. gerbes

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### gluing gerbes over a spectrum of a field

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### Mayer-Vietoris on Fibered Products

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### Constructing a stack (gerbe) from a connected groupoid

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### The Abelian Group of Equivalence Classes of Gerbes

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### Twisting an object P by an H-Torsor I

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### A Fourier-Mukai type duality for gerbes, torsors and their duals

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