# Homotopy Type Theory localization (changes)

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## Idea

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

## Definition

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

 \lambda g . g \circ (F(a)) F(a) : (C(a) \to X) \to (B(a) \to X)

is an equivalence . for all (a : A).

TODO: Localisation as a HIT?

## References

category: homotopy theory

Last revised on January 19, 2019 at 13:30:40. See the history of this page for a list of all contributions to it.