type family (changes)

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A family of types~~ indexed~~ is~~ by~~ a~~ another~~ function~~ type.~~$P$ from a type $A$ to a universe. Every term of $A$ corresponds to a type $P(A)$.

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:

$P(\star_X)\to \sum_{x:X}P(x) \to X$

universe Synthetic homotopy theory

category: type theory, homotopy theory

Last revised on January 19, 2019 at 10:49:03. See the history of this page for a list of all contributions to it.