Definition:Initial Object

Definition

Let $\mathbf C$ be a metacategory.

An initial object of $\mathbf C$ is an object $0 \in \mathbf C_0$ of $\mathbf C$ such that:

For all $C \in \mathbf C_0$, there is a unique morphism $0 \to C$.

Also known as

An initial object is also known as a coterminal object.

Also see

• Initial Object is Unique
• Definition:Terminal Object
• Definition:Zero Object

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 2.2$: Definition $2.9$