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In a new approach to [[foundations of mathematics]] called [[homotopy type theory]], the '''univalence axiom''' states:

: <math>(A = B) \simeq (A \simeq B)</math>

"In other words, identity is equivalent to equivalence. In particular, one may say that 'equivalent
types are identical'."<ref>{{cite book|author=Univalent Foundations Program|title=Homotopy Type Theory: Univalent Foundations of Mathematics|year=2013|publisher=Institute for Advanced Study|url=http://homotopytypetheory.org/book/|page=4}}</ref>

==References==
{{Reflist}}

[[Category:Homotopy theory]]
[[Category:Mathematical axioms]]

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