To formulate univalence as an axiom Voevodsky found a way to define " equivalences " syntactically that had the important property that the type representing the statement " f is an equivalence " was ( under the assumption of function extensionality ) (-1 )-truncated ( i . e . contractible if inhabited ).
12.
In theory, a word like " univalence " could be coined as a synonym, but as Gandalf notes, " certainty " or " decisiveness " are already in common use . " Ambivalence " would be a synonym for " uncertainty " or " indecisiveness " . ?! carrots?! 12 : 56, 6 May 2011 ( UTC)
13.
The participants also formulated a list of important open questions, such as whether the univalence axiom satisfies canonicity ( still open, although some special cases have been resolved positively ), whether the univalence axiom has nonstandard models ( since answered positively by Shulman ), and how to define ( semi ) simplicial types ( still open in MLTT, although it can be done in Voevodsky's Homotopy Type System ( HTS ), a type theory with two equality types ).
14.
The participants also formulated a list of important open questions, such as whether the univalence axiom satisfies canonicity ( still open, although some special cases have been resolved positively ), whether the univalence axiom has nonstandard models ( since answered positively by Shulman ), and how to define ( semi ) simplicial types ( still open in MLTT, although it can be done in Voevodsky's Homotopy Type System ( HTS ), a type theory with two equality types ).
15.
For instance, they noted that the groupoid model satisfies a rule they called " universe extensionality ", which is none other than the restriction to 1-types of the " univalence axiom " that Vladimir Voevodsky proposed ten years later . ( The axiom for 1-types is notably simpler to formulate, however, since a coherence notion of " equivalence " is not required . ) They also defined " categories with isomorphism as equality " and conjectured that in a model using higher-dimensional groupoids, for such categories one would have " equivalence is equality "; this was later proven by Ahrens, Kapulkin, and Shulman.
How to say univalence in Hindi and what is the meaning of univalence in Hindi? univalence Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
