# Homotopy Type Theory type family (Rev #8)

## Idea

A family of types indexed by another type.

## 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 $X$, the total space is $\sum_{(x:X)}P(x)$ and the fiber $P(\star_X)$. This gives the fibration:

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