Example 3.2.1.2. Let $f_0, f_1: X \rightarrow Y$ be morphisms of simplicial sets. Then $f_0$ and $f_1$ are homotopic (in the sense of Definition 3.1.5.1) if and only if they are homotopic relative to the empty subset $\emptyset \subset X$ (in the sense of Definition 3.2.1.1).
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