Remark 10.3.3.19. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $Q$ denote the collection of all quotient morphisms in $\operatorname{\mathcal{C}}$, and let $M$ denote the collection of all monomorphisms in $\operatorname{\mathcal{C}}$. Then $Q$ and $M$ are closed under isomorphism (see Corollary 10.3.2.12 and Remark 9.3.4.25), and $Q$ is left orthogonal to $M$ (Lemma 10.3.3.10). It follows that $\operatorname{\mathcal{C}}$ has images if and only if the pair $(Q,M)$ is a factorization system on $\operatorname{\mathcal{C}}$ (Definition 9.2.9.1).
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