# Homotopy Type Theory type family (Rev #4, changes)

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## Idea

A type family is a map P:X \to \mathcal U.

## Definition

A type family is a map $P:X \to \mathcal{U}$.

## Fibrations

Type families can be thought of as fibrations in classical homotopy theory. The base space is  P:X X \to \mathcal UX, the total space is $\sum_{(x:X)}P(x)$ and the fiber $P(\star_X)$. This gives the fibration:

$P(\star_X)\to \sum_{x:X}P(x) \to X$

## References

HoTT Book

category: type theory
category: homotopy theory

Revision on September 5, 2018 at 10:08:42 by Ali Caglayan. See the history of this page for a list of all contributions to it.