Generalized principal bundles and quotient stacks
Elena Caviglia

TL;DR
This paper generalizes the concept of principal bundles within a broad categorical framework, constructing quotient prestacks and proving their descent properties under certain conditions, advancing the theoretical understanding of stacks.
Contribution
It introduces a generalized notion of principal bundles in sites with pullbacks, and constructs quotient prestacks with descent properties, extending classical theory.
Findings
Quotient prestacks satisfy descent in subcanonical sites.
Explicit construction of quotient prestacks via presheaves of categories.
Generalization of principal bundles to abstract categorical contexts.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
