Homotopy Type Theory localization > history (Rev #8, changes)

Idea

Localization is the process of inverting a specified class of maps.

Definition

Consider a family $F:\prod_{(a:A)} B(a) \to C(a)$ of maps. We say that a type $X$ is $F$-local if the function

is an equivalence for all (a : A).

TODO: Localisation as a HIT?

Properties

References

• Modalities in homotopy type theory
• Localization in Homotopy Type Theory
• HoTT book