nLab h-initial object

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

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

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

Last revised on March 8, 2018 at 09:27:16. See the history of this page for a list of all contributions to it.