A correspondence between vector fields on differentiable stacks and stratified vector fields on orbit spaces is proven, enabling stacky versions of the Gauss lemma and Palais theorem.
Zung:Proper groupoids and momentum maps: linearization, affinity, and convexity, Ann
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Stratified vector fields on orbit spaces
A correspondence between vector fields on differentiable stacks and stratified vector fields on orbit spaces is proven, enabling stacky versions of the Gauss lemma and Palais theorem.