Homotopy Type Theory
type family (changes)

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Idea

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

Definition

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

Fibrations

Type families can be thought of as fibrations in classical homotopy theory. The base space is XX, the total space is (x:X)P(x)\sum_{(x:X)}P(x) and the fiber P( X)P(\star_X). This gives the fibration:

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

See also

universe Synthetic homotopy theory

References

HoTT Book

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