Weak Terminal Object

A weak terminal object in a Category $\mathcal{C}$ is like a Terminal Object, but with the existence property removed. Explicitly, $X$ is a weak terminal object if for every $A$, the space of maps $A\to X$ is an H-Proposition.

Properties

• A category $\mathcal{C}$ is a Preorder if and only if every object is weakly terminal.