Definition 2.27.
Let \(C\) be a category with pullbacks. A morphism \(f\colon U \to X\) is called an effective epimorphism if the cocone \(\check{C}^+_{\bullet}(f)\) is a colimit diagram, exhibiting \(X\) as the geometric realization \(\abs{\check{C}_{\bullet}(f)}\) of its Čech nerve. We denote by
\[\EffEpi(C) \, \subseteq \, \Ar(C)\]
the full subcategory spanned by the effective epimorphisms.