Homotopy Type Theory type family > history (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:

See also

universe Synthetic homotopy theory

References

HoTT Book