Definition 1.4.1.5 (Endomorphisms). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. An endomorphism in $\operatorname{\mathcal{C}}$ is a morphism $f: X \rightarrow X$ of $\operatorname{\mathcal{C}}$ for which the source and target of $f$ are the same. In this case, we will say that $f$ is an endomorphism of $X$.
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