Let $\Gamma=(\Gamma\_1\rightrightarrows \Gamma\_0), \Gamma’=(\Gamma’\_1\rightrightarrows \Gamma’\_0)$ be Lie groupoids and $\Gamma\_{\bullet} ,\Gamma’\_{\bullet}$ be the [simplicial manifolds associated to](https://arxiv.org/pdf/math/0401420v3.pdf) $\Gamma,\Gamma’$ respectively. 


Question : If the simplicial manifolds $\Gamma\_{\bullet}$ and $\Gamma’\_{\bullet}$ are isomorphic, then, does it imply that $\Gamma=(\Gamma\_1\rightrightarrows \Gamma\_0)$ and $ \Gamma’=(\Gamma’\_1\rightrightarrows \Gamma’\_0)$ are Morita equivalent?


Has this been mentioned anywhere?



Simplicial manifold associated to Lie groupoid
If the simplicial manifolds are isomorphic, then the groupoids are also isomorphic, since the nerve functor from groupoid objects in a category to simplicial objects in the same category is fully faithful.


So to answer your question: yes, but in a boring way.


