# nLab h-initial object

### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

## Models

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.

Last revised on March 8, 2018 at 04:27:16. See the history of this page for a list of all contributions to it.