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nLab > nLab General Discussions: The `simplex category' page

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    • CommentRowNumber1.
    • CommentAuthorBarber
    • CommentTimeDec 26th 2023
    I think the there is a typo here.

    Original text: The augmented simplex is a full subcategory of Cat on the free categories of....

    I believe it should be: The augmented simplex is a full subcategory of Cat *of* the free categories of....
    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 26th 2023

    Cat is the category of small categories and functors.

    Therefore, the current phrasing is correct: we take the full subcategory of Cat on the free categories of finite linear directed graphs, i.e., we take only those objects of Cat that are free categories of finite linear directed graphs.

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