Empty Set is Initial Object
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Theorem
Let $\mathbf{Set}$ be the category of sets.
Then the empty set $\O$ is an initial object of $\mathbf{Set}$.
Proof
Follows from Empty Mapping is Unique and the definition of initial object.
$\blacksquare$
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 2.2$: Example $2.11$: $1$