Example 4.7.6.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then $\operatorname{\mathcal{C}}$ is minimal in dimension $1$ if and only if, for every pair of objects $X,Y \in \operatorname{\mathcal{C}}$ and every pair of morphisms $f,g: X \rightarrow Y$ which are homotopic, we have $f = g$ (see Corollary 1.4.3.7).
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