$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary Let $\operatorname{\mathcal{C}}$ be a category which admits fiber products and let $f: X \rightarrow Y$ be a morphism in $\operatorname{\mathcal{C}}$. The following conditions are equivalent:


The morphism $f$ is a quotient morphism in the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ (in the sense of Definition


The morphism $f$ is a regular epimorphism: that is, it exhibits $Y$ as a coequalizer of the projection maps $X \times _{Y} X \rightrightarrows X$ (Definition