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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    Created, mainly with stuff from the overview.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    Add the clauses for variables

    v1, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    Add partial interpretation of contexts.

    v1, current

    • CommentRowNumber4.
    • CommentAuthordlicata335
    • CommentTimeNov 1st 2018

    To what extent is this proof of initiality intended to be constructive? I think that has some bearing on how the partial interpretations are treated. I think it should be possible to prove initiality in a constructive metalanguage, but maybe some shortcuts helpful for the intended audience are possible classically.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeNov 1st 2018

    I don’t immediately see anything that would make it nonconstructive.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeNov 1st 2018

    In particular, I think all the definitions of the partial interpretations should be expressed in purely category-theoretic language in the presheaf category [C op,Set][C^{op},Set], which is inherently constructive, especially because the internal logic of this category is not classical. Is there something that looks nonconstructive to you?

    • CommentRowNumber7.
    • CommentAuthorAlizter
    • CommentTime6 days ago

    What exactly is Tm V\Tm^{V} where VV is a finite set?

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTime5 days ago

    The VV-indexed power (for SetSet-enrichment) of the presheaf TmTm.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTime5 days ago

    Otherwise known as the product of VV copies of TmTm, or VTm\prod_{V} Tm.

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