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nLab > Latest Changes: fibered heterogeneous identity type

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  1. stub article

    Anonymouse

    v1, current

  2. added section on the use of John Major equality in characterizing the identity type of dependent pair types

    Anonymouse

    diff, v2, current

  3. added an alternate definition based upon the extensionality principle of dependent sum types, simplified previously added section to simply say that the two definitions are the same because of the extensionality principle of dependent sum types, and merged said section into the definitions section

    Anonymouse

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2023
    • (edited Oct 1st 2023)

    added the remark that:

    For better or worse, the terminology “John Major equality” was coinded in McBride 1999 §5.1.3 with reference to British political discussion of that time.

    Is it too late to find better terminology?

    (McBride offers: “…aspiring to be equal to others than oneself is the politics of envy. In much the same way, ≃\simeq forms equations…” What?!)

    diff, v3, current

  5. Added some inference rules

    Anonymouse

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2023

    Is it too late to find better terminology?

    How about calling it McBride equality?

    This would honor McBride’s mathematical insight while gracefully omitting the proliferation of his political comedy.

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeOct 2nd 2023

    How about calling it McBride equality?

    How about simply “heterogeneous equality”, which is the other terminology mentioned on the page? Unless this is ambiguous somehow?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2023

    I am not into this, but from the disambiguation entry heterogeneous equality I gather the need is felt to have a more specific term.

  9. About the ambiguity in “heterogeneous equality”, Mike Shulman wrote on the HoTT Zulipchat:

    Maybe we can distinguish the two with some more meaningful terminology. How about calling the version that depends on a path in the base, or an equality of types, indexed heterogeneous equality, and the other version (which admits a function to equalities of types) fibered heterogeneous equality? It’s the same relationship as other things we use those words for.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 7th 2023
    • (edited Oct 7th 2023)

    have renamed from “John Major equality” to “fibered heterogeneous identity type”

    adjusted the definition-section (here)

    (beyond just the type naming, I also changed the notation to be more straightforward throughout – for instance, generic terms of type AA are to be named “aa” and not “xx” and certainly not “bb”, given that an AA-dependent type “BB” plays a major role, too)

    For the time being I didn’t touch the following discussion of inference rules (starting here) except for a brief note highlighting the change in notation

    diff, v5, current

1 to 10 of 10

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