We consider the internalization of the usual notion of principal bundle in a site that has all pullbacks and a terminal object. We use this notion to consider the explicit construction of quotient prestacks via presheaves of categories of principal bundles equipped with equivariant morphisms in this abstract context. We then prove that, if the site is subcanonical and the underlying category satisfies some mild conditions, these quotient prestacks satisfy descent in the sense of stacks.
Keywords: principal bundles, quotient stacks, classifying stacks, canonical topology
2020 MSC: 18F20, 18F10, 18C40, 14A20, 18F15
Theory and Applications of Categories, Vol. 39, 2023, No. 20, pp 567-597.