Weak representations, representations up to homotopy, and VB-groupoids

Seth Wolbert

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arXiv · 1704.05019

Weak representations, representations up to homotopy, and VB-groupoids

Seth Wolbert

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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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Seth Wolbert. 2017-04-17. Weak representations, representations up to homotopy, and VB-groupoids. https://arxiv.org/abs/1704.05019

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