It is a known theorem that an internal equivalence of Lie groupoids (finite dimensional manifolds!) - that is an equivalence in the 2-category of Lie groupoids, smooth functors and transformations - ...
This is a continuation of my previous question. A) Morphisms in (1') are basically internal anafunctors, their compositions heavily use (and only) pullback/limit. B) Bibundles in (2) are basically ...
Recall the notion of Lie algebroid (n Lab, Wikipedia). One motivation for studying Lie algebroids is that they are infinitesimal versions of Lie groupoids, and Lie groupoids present stacks. In ...