Let $X$ be an Artin stack over $k=\mathbf{C}$. I've heard that $X$ has a topological realisation, but I've not been able to find an explicit decription.

My first guess would be: take a smooth cover $U\to X$ ($U$ is a scheme), then consider the simplicial space $$\cdots \ \longrightarrow U_\text{top}\times_XU_\text{top} \ \longrightarrow U_\text{top}$$ and take its geometric realisation. I think this gives the right answer when $X$ is a scheme or $X=BG$.

Is this guess correct? If not, what goes wrong and what is the correct answer?

Let $X$ be an Artin stack over $k=\mathbf{C}$. I've heard that $X$ has a topological realisation, but I've not been able to find an explicit decription.

My first guess would be: take a smooth cover $U\to X$ ($U$ is a scheme), then consider the simplicial space $$\cdots \substack{\rightarrow\\[-1em] \rightarrow \\[-1em] \rightarrow} U_\text{top}\times_XU_\text{top} \ \rightrightarrows U_\text{top}$$ and take its geometric realisation. I think this gives the right answer when $X$ is a scheme or $X=BG$.

Is this guess correct? If not, what goes wrong and what is the correct answer?