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nLab > Latest Changes: Subobject classifier

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  1.  
    • CommentRowNumber1.
    • CommentAuthoranuyts
    • CommentTimeNov 30th 2016

    I added a note to the article on the subobject classifier: “In type theory, the type corresponding to the subobject classifier is typically called Prop.”

    • CommentRowNumber2.
    • CommentAuthorspitters
    • CommentTimeNov 30th 2016

    I am not sure whether that’s very helpful. It’s not provable in type theory that it is. Even in HoTT, hProp is only a large SOC.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeNov 30th 2016

    If there is a type corresponding the subobject classifier, then it’s usually called Prop, and the type called Prop becomes a subobject classifier if we add a resizing axiom, so they are closely related and I think the connection is helpful to point out. But we could I guess be a bit more precise.

    • CommentRowNumber4.
    • CommentAuthorspitters
    • CommentTimeNov 30th 2016

    In Coq, we miss the axiom of description and extensionality for Prop. In HoTT, it’s called hProp, as you know.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeNov 30th 2016

    Yes, right, there’s more missing. But there’s still a close connection. (It’s called hProp in HoTT/Coq because “Prop” is taken by Coq, but in the HoTT Book we call it just Prop.)

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeDec 1st 2016

    I’ve updated the comment.

    • CommentRowNumber7.
    • CommentAuthorThomas Holder
    • CommentTimeJun 5th 2018

    I ventilated the issues around contractibility of Ω\Omega also a bit at subobject classifier.

    diff, v42, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2018
    • (edited Jun 5th 2018)

    made various further keywords hyperlinks, such as singleton, homotopy.

    diff, v43, current

  9. Made some grammatical/style fixes to sentence describing the power of subobject classifier in topos theory.

    Anonymous

    diff, v44, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 15th 2018

    touched the formatting, and moved the remark on subobject classifiers in presheaf toposes from being a standalone subsection after the example of GG-sets to being a remark after the example that it actually refers to

    diff, v45, current

1 to 10 of 10

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