[[!redirects type families]] [[!redirects Type families]] +--{.query} *This page is under construction. - Ali* =-- ## Idea ## ## 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: $$P(\star_X)\to \sum_{x:X}P(x) \to X$$ ## See also ## [[universe]] [[Synthetic homotopy theory]] ## References ## [[HoTT Book]] category: type theory category: homotopy theory