univalence मीनिंग इन हिंदी

उदाहरण वाक्य

1. Soon afterwards, Voevodsky proved that the univalence axiom implies function extensionality.
2. The "'univalence axiom "'states that this function is itself an equivalence.
3. These models have shown that the univalence axiom is independent from the excluded middle axiom for propositions.
4. HoTT adds the univalence axiom, which relates the equality of logical-mathematical propositions to homotopy theory.
5. It is a remarkable fact, fundamental to the theory of univalent functions, that univalence is essentially preserved under uniform convergence.
6. This enabled him to give a " syntactic " statement of univalence, generalizing Hofmann and Streicher's " universe extensionality " to higher dimensions.
7. The problem of finding a constructive way of interpreting the rules of the Martin-Lof type theory that in addition satisfies the univalence axiom and canonicity for natural numbers remains open.
8. It was originally used by Vladimir Voevodsky to refer to his vision of a foundational system for mathematics in which the basic objects are homotopy types, based on a type theory satisfying the univalence axiom, and formalized in a computer proof assistant.
9. This means, for example, that it would be difficult to formulate univalence in this theory there are contractible types in each of the V i but it is unclear how to declare them to be equal since there are no identity types connecting V i and V j for i ` " j.
10. Here, type theory is extended by the univalence axiom, ('equivalence is equivalent to equality') which permits homotopy type theory to be used as a foundation for all of mathematics ( including set theory and classical logic, providing new ways to discuss the axiom of choice and many other things ).