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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 8th 2020

    Removed an incorrect historical claim (Dwyer and Kan did throughly investigate relative categories already in 1980s, way before 2000s).

    Added a section about model structures.

    diff, v3, current

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeJun 23rd 2021

    Added to the idea section that relative categories are sometimes used to capture the notion of a category with a distinguished wide subcategory of morphisms that should be preserved by functors.

    I also added a section on the fact that relative categories are enriched categories.

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 23rd 2021

    It looks like it’s talking about the same thing as F-category.

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeJun 23rd 2021

    Added F-category and marked simplicial set as related concepts

    diff, v7, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 23rd 2021

    I have touched the formatting (e.g. hyperlinks of and to references), reorganized the TOC (Definitions under Definitions, Properties under Properties etc.). Also added a cross link back from F-category.

    diff, v8, current

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 23rd 2021

    Oh sorry, my bad, I think I really meant the closely related concept of M-category. I’ll add some links.

    • CommentRowNumber7.
    • CommentAuthorHurkyl
    • CommentTimeJun 25th 2021

    Reordered the properties so that the definition of RelCat comes before the reformulation as PairSet-Cat. Included a link to M-category in the enriched category formulation.

    diff, v10, current

    • CommentRowNumber8.
    • CommentAuthorHurkyl
    • CommentTimeSep 27th 2022

    Remarked that the semi-saturation condition picks out the relative categories that remain monomorphisms in the 2-category of categories.

    diff, v13, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMay 1st 2023
    • (edited May 1st 2023)

    Under “References” (here) I rearranged slightly to make clear that the terminology “relative category” is due to Barwick & Kan 2012, while it is the the basic idea that goes back, at least, to Dwyer & Kan 1980

    diff, v17, current