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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 16th 2013

    Created partial map classifier, but itex won’t make harpoons even though this page claims it can.

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeApr 16th 2020

    Added a construction of the partial map classifier as the dependent product along 1Ω1 \to \Omega.

    diff, v12, current

    • CommentRowNumber3.
    • CommentAuthorHurkyl
    • CommentTimeJun 11th 2023
    • (edited Jun 11th 2023)

    Added a section on relative partial maps. Mainly, I wanted to record the construction of the partial map classifier of a slice topos and the fact it represents a presheaf of commutative squares.

    diff, v16, current

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeJun 11th 2023

    Added an unpacked version of the definition of the classifier, in the similar style to how subobject classifiers are defined.

    diff, v17, current

    • CommentRowNumber5.
    • CommentAuthorHurkyl
    • CommentTimeJun 12th 2023
    • (edited Jun 12th 2023)

    Is the higher inductive-inductive type definition added by anonymous edit #14 correct? While admittedly I have little familiarity with HITs, the elements of the definition given don’t look like they’re trying to define a partial map classifier. And even I’m wrong and the gist is right, I think it’s riddled with typos.

    It feels really out of place anyways.

    • CommentRowNumber6.
    • CommentAuthormaxsnew
    • CommentTimeJun 12th 2023

    It looks like an (incorrect?) transcription of the construction in where they construct the free omega-CPO as a QIT and use this as a partial map classifier that works without countable choice.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2023

    Maybe best to delete the section and instead leave a concrete pointer in the list of references to where the reader may find partial map classifier discussed in type theory.

    • CommentRowNumber8.
    • CommentAuthorHurkyl
    • CommentTimeJun 13th 2023

    Okay, I’ve removed the section. I left the references that were added in the edit, although I’ve changed the description a little bit, since I’m not confident what’s described in the references, interpreted in the context at hand, actually reproduces the concept discussed on this page.

    diff, v20, current