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differentiable stack
In differential geometry, a differentiable stack is a stack over the category of differentiable manifolds (with the usual open covering topology) which admits an atlas. In other words, a differentiable stack is a stack that can be represented by a Lie groupoid.
==Connection with Lie groupoids==
Every Lie groupoid Γ gives rise to a differentiable stack that is the category of Γ-torsors. In fact, every differentiable stack is of this form. Hence, roughly, "a differentiable stack is a Lie groupoid up to Morita equivalence."
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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