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Results tagged with homotopy-type-theory
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user 114245
The homotopy interpretation of constructive dependent type theory, the univalence axiom, higher inductive types, internal languages of higher toposes, univalent foundations for mathematics, and implementations of such theories in proof assistants.
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The role of univalence in the homotopy interpretation of type theory
In Martin-Löf type theory with identity eliminator
$$
J :
\prod_{B:\prod_{x,y:A}(x=y)\to\mathcal{U}}\left(
\prod_{x:A}B(x,x,\mathrm{refl}_x)\to
\prod_{x,y:A}\prod_{p:x=y}B(x,y,p)
\right)
$$
satisfy …
- 213