Fat Lie theory defines fat extensions and abstract 2-term ruths with one-to-one correspondences to general linear PB-groupoids and core-transitive double groupoids, upgrading prior equivalences to category equivalences.
Weak representations, representations up to homotopy, and VB-groupoids
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abstract
In this paper, I introduce weak representations of a Lie groupoid $G$. I also show that there is an equivalence of categories between the categories of 2-term representations up to homotopy and weak representations of $G$. Furthermore, I show that any VB-groupoid is isomorphic to an action groupoid associated to a weak representation on its kernel groupoid; this relationship defines an equivalence of categories between the categories of weak representations of $G$ and the category of VB-groupoids over $G$.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Fat Lie Theory
Fat Lie theory defines fat extensions and abstract 2-term ruths with one-to-one correspondences to general linear PB-groupoids and core-transitive double groupoids, upgrading prior equivalences to category equivalences.