Homotopy Type Theory
type family (Rev #8, changes)

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Idea

A family of types indexed by another type.

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

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.