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nLab > Latest Changes: unit type

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  1. clarifying the categorical semantics section

    Anonymous

    diff, v13, current

  2. adding section about positive and negative unit types in dependent type theory with typal computation and uniqueness rules, formalised in natural deduction

    Anonymous

    diff, v14, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2022
    • (edited Dec 17th 2022)

    I have hyperlinked more of the technical terms.

    Also touched the wording in some places, for streamlining.

    diff, v16, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2023
    • (edited Jan 3rd 2023)
    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeMar 27th 2023

    added a section about the unit type as a univalent universe

    diff, v20, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2023

    Dear Anonymous Guest,

    The first sentence in your edit is

    The unit type could also be represented as a univalent universe.

    Instead of “could” you mean “can” or “may”. Instead of “represented” you mean “regarded”.

    The last sentence of your addition is:

    The extensionality principle for the unit type then is simply the univalence axiom:

    It hardly “is the univalence axiom”. Rather, it’s a completely degenerate variant oft it.

    Even if we were to fix these sentences, I have trouble seeing what is useful about your paragraph.

    Why are you adding such material, what motivates you? And why are you still hiding in anonymity?

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeMar 27th 2023

    added a paragraph explaining why it is useful to consider the unit type as a universe: universes in type theory correspond to regular and inaccessible cardinals in set theory

    also added a sentence explaining that yes indeed the unit type represents a trivial universe where every type is contractible.

    diff, v21, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2023

    Thanks for reacting, I appreciate it. That looks better.

1 to 8 of 8

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