# Homotopy Type Theory localization (Rev #6, changes)

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## Idea

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

## Definition

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

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

is an equivalence.

## References

category: homotopy theory

Revision on October 10, 2018 at 19:21:02 by Ali Caglayan. See the history of this page for a list of all contributions to it.