Terminal Object

An object $T:\mathcal{C}$ in a Category $\mathcal{C}$ is a terminal object if for any other object $X:\mathcal{C}$, there exists a unique map $!:X\to T$.

Properties

• Terminal objects are Limits of diagrams over the Initial Category.

• A category $\mathcal{C}$ has a Terminal Object if and only if the unique functor $!:\mathcal{C}\to 1$ to the Terminal Category has a Right Adjoint.