Higher Covering Maps, Deck Transformations, and Yoneda in an ∞-Topos
Event details
| Date | 23.10.2025 |
| Hour | 16:00 › 17:00 |
| Speaker | Virgile Constantin |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
A classical and elementary result in topology identifies the group of deck transformations of a normal covering map (with discrete fibers) with a quotient of the fundamental group. In this talk, I will explain how to internalize this result in a fixed ∞-topos E, obtaining an isomorphism of group objects in E. Even better, for coverings with (n-1)-truncated fibers, we obtain an analogous isomorphism of n-group objects between the deck transformation n-group and a suitable quotient of the fundamental n-group.
The key input is an internal form of the Yoneda lemma (and embedding) in E; I will present and motivate its formulation, and highlight its central role in the proof. As a direct corollary, we obtain a uniqueness result for quotients of higher groups.
The talk is designed to be accessible: no prior knowledge of ∞-topoi is necessary.
Practical information
- Informed public
- Free
Organizer
- Virgile Constantin
Contact
- Maroussia Schaffner