Homotopy Type Theory
identity type

Idea

The identity type has elements that are witnesses to the “sameness” of elements.

Definition

The identity type = A:AA𝒰=_A : A \to A \to \mathcal{U} can be defined as the inductive type? with the following constructor:

  • for any a:Aa:A, an element refl A:a= Aarefl_A: a=_A a

See also

higher inductive type

References

HoTT book

category: type theory

Last revised on October 11, 2018 at 08:59:46. See the history of this page for a list of all contributions to it.