Homotopy Type Theory type family > history (Rev #3)

Idea

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

Definition

Fibrations

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

References

HoTT Book