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nLab > Latest Changes: right-connected double category

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1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorBryceClarke
    • CommentTimeJan 31st 2023

    Created a new page on right-connected double categories, with a basic definition and reference. I intend to fill in with more details and examples soon.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 31st 2023
    • (edited Jan 31st 2023)

    I have changed

    “identity map” to “identity-assigning map”

    and

    “codomain map” to “codomain-assigning map”.

    Also added

    hyperlink to “right adjoint”

    plural redirect: [[!redirects right-connected double categories]]

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 6th 2023

    Added the definition of left-connected double category, and another example.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 6th 2023

    Unpacked the definition of a right-connected double category in explicit terms.

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 6th 2023

    Added a basic proposition that every right-connected double category admits a double functor to the double category of squares.

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 6th 2023

    Added an Idea section, another basic example, and a new proposition stating the adjoint triple between the 22-category of right-connected double categories and CatCat.

    diff, v6, current

    • CommentRowNumber7.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 8th 2023

    Rearranged some content, added the example of monomorphisms and pullback squares, added more detail to several areas.

    diff, v8, current

    • CommentRowNumber8.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 8th 2023

    Added the “main theorem” which characterises those right-connected double categories which arise from algebraic weak factorisation systems. Also fixed some examples.

    diff, v9, current

    • CommentRowNumber9.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 8th 2023

    Added several more examples, and two more basic properties: one characterising the thin right-connected double categories, and the other concerning orthogonal factorisation systems.

    diff, v10, current

1 to 9 of 9

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