Example 5.8.
For \(T= \An\), the map \(S^0 \to *\) is an effective epimorphism (as it is a surjection on path components), but it is not an epimorphism: the pushout of \(S^0 \to *\) along itself is \(S^1\), which is not isomorphic to \(*\).
Higher Topos Theory Section 5.1: Epimorphisms and acyclic maps
Example 5.8.
For \(T= \An\), the map \(S^0 \to *\) is an effective epimorphism (as it is a surjection on path components), but it is not an epimorphism: the pushout of \(S^0 \to *\) along itself is \(S^1\), which is not isomorphic to \(*\).