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nLab > Latest Changes: univalent dagger category

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  1. copied from HoTT wiki

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2022
    • (edited Jun 6th 2022)

    I have hyperlinked induction on identity, but please check if that’s what you need here.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeAug 31st 2022

    Added definition, discussion, and redirects for both dagger-precategories and univalent dagger categories. Include definition of unitary isomorphism. Note that the univalence axiom is necessary for standard examples to be univalent.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeAug 31st 2022

    Add reference to The Univalence Principle monograph.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeSep 1st 2022

    One should also be able to define the additional dagger categories:

    A skeletal dagger category is a dagger precategory for which the canonical function (A=B)→|A≅ †B|(A = B) \to \vert A \cong^\dagger B \vert is an equivalence.

    A strict dagger category is a dagger precategory whose type of objects is 0-truncated. (these are the dagger categories in set-theoretic foundations)

    A gaunt dagger category is a strict univalent dagger category, or equivalently a skeletal univalent dagger category.

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