Principal 2-bundles and quotient 2-stacks
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913264741384192 |
|---|---|
| author | Caviglia, Elena |
| author_facet | Caviglia, Elena |
| contents | We generalize principal bundles and quotient stacks to the two-categorical context of bisites. We introduce a notion of principal 2-bundle that makes sense for a 2-category with finite flexible limits, endowed with a bitopology. We then use principal 2-bundles to explicitly construct quotient-pre-2-stacks, which are the analogues of quotient stacks one dimension higher. In order to perform this construction, we prove that principal 2-bundles are closed under iso-comma objects and we restrict ourselves to (2,1)-categories. Finally, we prove that, if the bisite is subcanonical and the underlying (2,1)-category satisfies some mild conditions, quotient pre-2-stacks are 2-stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Principal 2-bundles and quotient 2-stacks Caviglia, Elena Category Theory Algebraic Geometry 18F20, 18F10, 18N10, 14A20 We generalize principal bundles and quotient stacks to the two-categorical context of bisites. We introduce a notion of principal 2-bundle that makes sense for a 2-category with finite flexible limits, endowed with a bitopology. We then use principal 2-bundles to explicitly construct quotient-pre-2-stacks, which are the analogues of quotient stacks one dimension higher. In order to perform this construction, we prove that principal 2-bundles are closed under iso-comma objects and we restrict ourselves to (2,1)-categories. Finally, we prove that, if the bisite is subcanonical and the underlying (2,1)-category satisfies some mild conditions, quotient pre-2-stacks are 2-stacks. |
| title | Principal 2-bundles and quotient 2-stacks |
| topic | Category Theory Algebraic Geometry 18F20, 18F10, 18N10, 14A20 |
| url | https://arxiv.org/abs/2403.09379 |