Notation 4.4.3.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We let $\pi _0( \operatorname{\mathcal{C}}^{\simeq } )$ denote the set of connected components of the Kan complex $\operatorname{\mathcal{C}}^{\simeq }$. Note that $\pi _0( \operatorname{\mathcal{C}}^{\simeq } )$ can be identified with the set of isomorphism classes of objects of $\operatorname{\mathcal{C}}$ (that is, the quotient of the set of objects of $\operatorname{\mathcal{C}}$ by the equivalence relation of isomorphism).
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