# 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.