In the page https://ncatlab.org/nlab/show/Lie+2-groupoid the Lie 2-groupoid is defined as the 2 truncated $\infty$-Lie groupoid.

I am not much comfortable with the language of higher category theory yet. But after reading some links in ncatlab I felt *Lie 2-Groupoid is the same as a 2-groupoid( a 2 category whose both 1 morphisms and 2 morphisms are invertible) internal to the category of smooth manifolds*.

**Am I right??**

Now on the page https://ncatlab.org/nlab/show/infinity-Chern-Weil+theory+introduction#Cech2Cocycles it is mentioned that the Cech groupoid of a manifold $X$ with a cover $U_{\alpha}$ can be thought as a Lie 2 -groupoid by considering the third stage of the full Cech Nerve.

I can understand that the Cech Groupoid $(\sqcup{U_{i}\cap U_{j}}\rightrightarrows \sqcup U_k)$ is a Lie groupoid. But I am not able to understand how $(\sqcup{U_{i}\cap U_{j}\cap U_{k}} \substack{\textstyle\rightarrow\\[-0.6ex] \textstyle\rightarrow \\[-0.6ex] \textstyle\rightarrow} \sqcup{U_{i}\cap U_{j}}\rightrightarrows \sqcup U_k)$ is a Lie 2-groupoid (in the sense I have understod the definition of Lie 2-groupoid). Infact I am not able to guess what can be the 2-morphisms in $(\sqcup{U_{i}\cap U_{j}\cap U_{k}} \substack{\textstyle\rightarrow\\[-0.6ex] \textstyle\rightarrow \\[-0.6ex] \textstyle\rightarrow} \sqcup{U_{i}\cap U_{j}}\rightrightarrows \sqcup U_k)$ (when described as a Lie 2-groupoid).

So is my understanding of Lie 2-groupoid wrong? If not then what is *the 2-categorical description* of $(\sqcup{U_{i}\cap U_{j}\cap U_{k}} \substack{\textstyle\rightarrow\\[-0.6ex]
\textstyle\rightarrow \\[-0.6ex]
\textstyle\rightarrow}
\sqcup{U_{i}\cap U_{j}}\rightrightarrows \sqcup U_k)$?

Thanks in Advance.

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