nLab
cofiber type
Contents
Definition
In dependent type theory with identity types, function types, and dependent function types, given a function , the cofiber type or cofibre type of is the higher inductive type generated by
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a term
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a function
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a dependent function
In essence, the cofiber type takes the image of the function and makes it contractible, but leaves the rest of the codomain untouched.
Induction rules
Formation rules for cofiber types:
Introduction rules for cofiber types:
Elimination rules for cofiber types:
Computation rules for cofiber types:
Uniqueness rules for cofiber types:
Examples
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The cofiber type of the unique function out of the empty type to any type is the type .
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The cofiber type of a function out of the unit type to any type is equivalent to .
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The cofiber type of the identity function on a type is the cone type of .
See also
References
- Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program, Institute for Advanced Study, 2013. (web, pdf)
Last revised on July 8, 2023 at 12:58:40.
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