Principal bundle groupoids, their gauge group and their nerve

We consider groupoids in the category of principal bundles, which we call principal bundles groupoids. We build their ajoint bundle groupoids, which we interpret as vector bundle groupoids, widely discussed in the literature. We describe their nerves, which are simplicial objects in the category of principal bundles. Applying this construction to pair groupoids enables us to define the gauge group of the nerve of a gauge groupoid as the gauge group of a principal bundle and to describe the corresponding gauge transformations.

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