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nLab > Latest Changes: set-level foundations

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeSep 1st 2022

    I think we need a name for “foundational systems in which all basic objects behave like sets”, e.g. set theories and extensional type theories. This is just a proposal, feel free to suggest others.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 1st 2022

    It might also be useful to have a name, and maybe even a page, for the complement. Maybe “higher foundations”?

    • CommentRowNumber3.
    • CommentAuthorUlrik
    • CommentTimeSep 1st 2022

    Add a link to and some remarks about the connection to sets cover.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUlrik
    • CommentTimeSep 1st 2022

    Re 2: Maybe “higher-level foundations” would be even more parallel?

  5. added the elementary theories of the bicategory of categories and the (2,1)-category of groupoids to the list of examples of foundations which are not set-level

    Anonymous

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeSep 2nd 2022

    Added a link to ETCC.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeSep 2nd 2022

    Removed list of higher foundations to go on higher foundations.

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeSep 2nd 2022

    Note that a higher foundation can still satisfy “sets cover” and remain “higher”.

    diff, v5, current

  9. adding Lean to list of examples

    Anonymous

    diff, v6, current

1 to 9 of 9

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