Kerodon

Notation 3.5.6.6. Let $X$ be a Kan complex and let $n \geq 0$ be an integer. We will see later that there exists a morphism of Kan complexes $f: X \rightarrow Y$ which exhibits $Y$ as a fundamental $n$-groupoid of $X$ (Theorem 3.5.6.17). It follows from Proposition 3.5.6.5 that $Y$ is unique up to (canonical) isomorphism and depends functorially on $X$. To emphasize this dependence, we will typically denote the simplicial set $Y$ by $\pi _{\leq n}(X)$, and refer to it as the fundamental $n$-groupoid of $X$.