20250321 Differentiable Stacks V

Last week, we saw how Lie groupoids give rise to differentiable stacks and vice-versa. This talk answers the following question: How to detect an isomorphism between differentiable stacks from their corresponding Lie groupoids? This requires the introduction of Morita equivalences and G-bibundles. We show that Morita equivalent Lie groupoids correspond to isomorphic differentiable stacks. For this, we investigate what happens to morphisms of stacks under the above correspondence. If time remains, we give a criterion to detect Morita equivalent maps and explain their relation to G-bibundles.