CatDat

• Notation: $F$
• Category: category of small categories

Let $I$ denote the walking morphism and $\Idem$ denote the walking idempotent. In this entry, we consider the functor $F : I \to \Idem$ that sends the universal morphism $! : 0 \to 1$ to the universal idempotent $e : 0 \to 0$ and view $F$ as a morphism in $\Cat$. It provides an example of a strong epimorphism which is not strict.