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  1. starting this article based upon a suggestion by Mike Shulman on the discussion thread for extensional type theory, that from now on “extensional” should only be used for definitionally extensional type theories on the nLab

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    Thanks!

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    Is cubical type theory with equality reflection a thing? I mean, I suppose one could write it down, but has anyone done it?

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeSep 3rd 2022

    The authors of A Cubical Language for Bishop Sets briefly mentioned the possibility of adding an equality reflection rule to their cubical type theory in section 8.2 of their article.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeSep 4th 2022

    Added list of set-level intensional type theories, taken from extensional type theory.

    diff, v3, current