For the category of simpicial animas(simplicial $\infty$-groupoids if you like) $sAn$, we have the evaluation functor $\text{ev}_n:sAn\rightarrow An$ with a left adjoint $\text{const}_n$ and the realization functor $|\ |:sAn\rightarrow An$ with a right adjoint being the Rezk nerve.

I wonder why $\Omega |\text{const}_1 X|$ is $X$. This is used in the (4.1.27) in the Lecture notes: Lecture Notes on Algebraic K-Theory.

I can't even give a direct description for $\text{const}_1X$. Is this something concerning the theory of Segal spaces...?