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"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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Phenomena of gerbes

What is your favourite example of Gerbes? I would like to know Where do we find Gerbes in "nature"? The examples could vary from String theory to Galois theory. … For example my favourite examples of Gerbes are Nori fundamental gerbe, and that Tannakian categories could be described, in cohomological terms, by the gerbe of its fibre functors. What is yours? …