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• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 7th 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.

• 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.

• 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

• 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.

• 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.

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