Homotopy Type Theory
univalence axiom (Rev #4, changes)

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The univalence axiom for a universe UU states that for all A,B:UA,B:U, the map

(A= UB)Equiv(A ,B) (A=_U B) \to Equiv(A,B) (A\simeq B)

defined by path induction? , is an equivalence. So we have

(A= UB)(AB). (A=_U B) \simeq (A \simeq B).

why not use infix notation ABA \simeq B here? otherwise it would seem more natural to use Id U(A,B) Id_U(A, B) rather than (A= UB) (A=_U B) .

So we have

(A= UB)(AB). (A=_U B) \simeq (A \simeq B).

Revision on March 3, 2014 at 14:14:01 by Mike Shulman. See the history of this page for a list of all contributions to it.