A family of types indexed by another type.

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

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:

universe Synthetic homotopy theory

HoTT Book

Revision on September 20, 2018 at 19:14:50 by Ali Caglayan. See the history of this page for a list of all contributions to it.