Year: 2025
Type: article
Abstract: We introduce higher analogs for cleavages in the context of (Kan) simplicial fibrations. We apply them to obtain geometric models for representations up to homotopy of (higher) Lie groupoids. Concretely, we set an equivalence between representations up to homotopy and simplicial vector bundles endowed with a cleavage. Our result is an incarnation of the Higher Grothendieck Correspondence, it can be seen as a relative Dold–Kan Theorem and extends earlier work of Gracia-Saz and Mehta on VB-groupoids.
DOI: 10.1093/imrn/rnaf128
Authors: Matias del Hoyo, Giorgio Trentinaglia
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410634745