The role of univalence in the homotopy interpretation of type theory – mathoverflow.net

The role of univalence in the homotopy interpretation of type theory – mathoverflow.net

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In Martin-Löf type theory with identity eliminator $$ J : \prod_{B:\prod_{x,y:A}(x=y)\to\mathcal{U}}\left( \prod_{x:A}B(x,x,\mathrm{refl}_x)\to \prod_{x,y:A}\prod_{p:x=y}B(x,y,p) \right) $$ ...

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