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

Showing changes from revision #3 to #4: Added | Removed | Changed

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

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

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

$(A=_U B) \simeq (A \simeq B).$

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

So we have

$(A=_U B) \simeq (A \simeq B).$

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.