Let $\mathcal{M}\_{g,n}$ be the moduli stack over $\mathbb{Q}$ of smooth curves of genus $g$ with $n$ marked points. I've seen in many sources an exact sequence:


$$1\rightarrow\pi\_1((\mathcal{M}\_{g,n})\_{\overline{\mathbb{Q}}})\rightarrow\pi\_1(\mathcal{M}\_{g,n})\rightarrow\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\rightarrow 1$$


Can someone point to a book/paper where this sequence is proven to be exact?



reference request for homotopy exact sequence of moduli stacks of curves
V. Zoonekynd, The fundamental group of an algebraic stack, arxiv.org math.AG/0111071


B. Noohi (2004). FUNDAMENTAL GROUPS OF ALGEBRAIC STACKS. Journal of the Institute of Mathematics of Jussieu, 3, pp 69­-103


