Definition 10.3.5.10. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be regular $\infty $-categories. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is regular if it preserves finite limits and carries quotient morphisms of $\operatorname{\mathcal{C}}$ to quotient morphisms of $\operatorname{\mathcal{D}}$.
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