Definition 1.4.6.12 (The Fundamental Groupoid of a Kan Complex). Let $X$ be a Kan complex. It follows from Proposition 1.4.6.10 that the homotopy category $\mathrm{h} \mathit{X}$ of Definition 1.4.5.3 is a groupoid. We will denote this groupoid by $\pi _{\leq 1}(X)$ and refer to it as the fundamental groupoid of $X$.
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