nLab
homotopy localization

Homotopy localisation

Idea

Given a site C equipped with an interval object *⨿*[i 0,i 1]I the homotopy localization of an (∞,1)-category of (∞,1)-sheaves Sh (C) on C is the (∞,1)-categorical localization of Sh (C) at the morphisms of the form

XId×i 0X×I.X \stackrel{Id \times i_0}{\to} X \times I \,.

David Roberts: From what I understand of the work on A 1 homotopy, the localisation is of morphisms of the form X×IX.

Urs Schreiber: but should that make a difference?

Examples