Initial (category theory)

See initial and final compared (category theory) for this definition and its dual side by side

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Created to move towards nets and generalised convergence/limits.

• Demote once examples and co are added

Definition

Let $\mathcal{C}$ be a category and let $S\in\text{Ob}(\mathcal{C})$ be any object of $\mathcal{C}$. Then $S$ is initial in $\mathcal{C}$ if:

• For all $A\in\text{Ob}(\mathcal{C})$
  • there exists a unique morphism: $\xymatrix{S \ar[r] & A}$

See also

• final (AKA: terminal)