nLab
covariant type family
Context
Directed homotopy type theory
Contents
Definition
In simplicial homotopy type theory, given a type and a type family
let us define the type family
as
where is the directed interval primitive, is the -simplex probe shape, and is its boundary.
Then a covariant type family over is a type family
such that given elements , , , and , the type
is a contractible type.
Properties
Theorem
Given a Segal type , a type family
is a covariant type family if and only if for all elements , and , there is a unique lifting of that starts at ; or equivalently, that the type
is contractible.
References
Last revised on May 23, 2023 at 14:52:10.
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