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I'm reading these Behrend's notes on cohomology of stacks, and I can't get over a detail in the fourth page. Let $X_\bullet=(X_1\rightrightarrows X_0)$ be a Lie groupoid and let $\mathcal{N}$ be its ...

[This is a repost, because I've written the wrong page number in the previous version of this question. I'm sorry] I'm currently reading "Orbifolds as stacks" by Eugene Lerman and I'm stuck ...

I'm reading these Behrend's notes on cohomology of stacks, and I can't get over a detail in the fifth page. Let $X_\bullet=(X_1\rightrightarrows X_0)$ be a Lie groupoid and let $\mathcal{N}$ be its ...

Let $G$ be a Lie group and $\mathcal{D}$ be a differentiable stack (I am also ok to start with a topological group and topological stack). I have seen someone mentioning somewhere that the notion of ...

I'm interested specifically in an inverse image functor between differentiable stacks, ie. stacks coming from Lie groupoids. Specifically, if I have a morphism of Lie groupoids $H\to G$ and I have a ...