Definition:Initial Object

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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