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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 1st 2011
    • (edited Sep 26th 2012)

    started bracket type, just for completeness, but don’t really have time for it

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 1st 2011

    had the chance to add a bit more to bracket type: now there is an Idea-section a Semantics-section.

    I have also added links to bracket type to relevant entries, in particular to types and logic - table.

    Experts please check. I am pretty sure I know what I am talking about here, but I may not be using language in the standard way.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 1st 2011

    I am somewhat surprised that the idea of “bracket types” is not already in the original articles on propositions as types. I had thought that taking bracket types is implicitly understood all along.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeDec 3rd 2011
    Thanks! I edited bracket type a bit. Bracket types were actually already referred to at propositions as types, only not by that name -- in the final paragraph of the Idea section under the phrase "propositions as some types". I added extra clarification there as well.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2012
    • (edited Sep 26th 2012)

    I have added to bracket type a brief section Definition in homotopy type theory with the definition of supp(A)supp(A).

    Also added four references on this. I see in Mike’s lectures the construction is attributed to Lumsdaine. However in the recent post by Brunerie, it seems to be attributed to Voevodsky. I don’t know. The entry currently does not cite Lumsdaine yet, but probably it should.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeSep 26th 2012
    • (edited Sep 26th 2012)

    Voevodsky defined it, as Guillaume said, “using impredicative quantification and resizing rules” (and also univalence). I believe his definition simply mimics the classical proof that a (1-)topos is a regular category — univalence plus a resizing rule is just the way that you get a subobject classifier in HoTT.

    The definition as an HIT is what is due to Peter Lumsdaine.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 26th 2017

    I added the recursion principle for supp(A)supp(A). I also added to the notations for the bracket type. We’re up to 6 now.

  1. fixed HTML entities to UTF-8 characters in Agda snippet


    diff, v17, current

  2. added section relating propositional truncations to localizations.


    diff, v23, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 20th 2023

    added pointer to

    and doi-link to:

    diff, v24, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeFeb 21st 2023

    added pointer to:

    Have only scanned the first few pages, but: Is this not secretly rediscovering the notion of anafunctor?

    diff, v25, current

    • CommentRowNumber12.
    • CommentAuthorGuest
    • CommentTimeMar 10th 2023

    added definition of bracket type using a type of all propositions.

    diff, v27, current

  3. Added definition of propositional truncation as a sequential colimit and added the reference where the definition came from


    diff, v31, current