[[!redirects type families]] [[!redirects Type families]] ## 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 $X$, the total space is $\sum_{(x:X)}P(x)$ and the fiber $P(\star_X)$. This gives the fibration: $$P(\star_X)\to \sum_{x:X}P(x) \to X$$ ## References ## HoTT Book