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nLab > Latest Changes: propositional equality

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  1. starting page on propositional equality, to contrast with judgmental equality and typal equality (the latter which redirects to identity type)

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2022

    Thanks for all your additions!

    One thought on this entry:

    The term “two-level type theory” right in the first sentence (here) would deserve to be hyperlinked. But checking what we have, I see that our entry two-level type theory has not quite the right content for the present purpose. Maybe that entry should be disambiguated a little?

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeNov 9th 2022

    Urs,

    Thanks for your comment. I think a more appropriate name for that notion might be “two-layer type theory”. Riehl and Shulman called their type theory with shapes a type theory with three-layers in section 2 of arXiv:1705.07442, so an article on layered type theory could be created, with two-level type theory, typed predicate logic, type theory with shapes, simplicial type theory, and cubical type theory all as examples of layered type theory.

  4. adding link to layered type theory

    Anonymous

    diff, v4, current

  5. replaced phrase

    In any two-layered type theory with a layer of types and a layer of propositions

    with

    In any predicate logic over type theory

    Anonymous

    diff, v4, current

  6. split context not needed

    Anonymous

    diff, v7, current

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