nLab h-initial object

Definition

Let $\mathcal{C}$ be an (∞,1)-category. An object $x$ in $\mathcal{C}$ is said to be $h$-initial if it defines an initial object in the homotopy category $Ho(\mathcal{C})$.

Dually, an object is called $h$-terminal if it defines a terminal object in $Ho(\mathcal{C})$.

To be distinguished from the concept of initial object in an (∞,1)-category and terminal object in an (∞,1)-category.