The initial set is the pair $\webleft (\emptyset ,\webleft\{ \iota _{A}\webright\} _{A\in \text{Obj}\webleft (\mathsf{Sets}\webright )}\webright )$ consisting of:
- The Limit. The empty set $\emptyset $ of Definition 2.3.1.1.1.
- The Cone. The collection of maps
\[ \webleft\{ \iota _{A}\colon \emptyset \to A\webright\} _{A\in \text{Obj}\webleft (\mathsf{Sets}\webright )} \]
given by the inclusion maps from $\emptyset $ to $A$.