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nLab > Latest Changes: boolean domain

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1 to 13 of 13

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2023

    added the following redirects (which used to point to truth value):

      [[!redirects boolean]]
  [[!redirects booleans]]

  [[!redirects Boolean]]
  [[!redirects Booleans]]

    and to

      [[!redirects Bit]]

    and cross-linked with bit and more terms (such as top and bottom)

    added reference to the Wikipedia entry

    will next add inference rules for Bool as an inductive type…

    diff, v19, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2023

    spelled out (here) the type inference rules.

    added pointer to

    diff, v19, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2023

    added pointer to:

    diff, v20, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2023

    added a paragraph (here) making explicit that Bit≃S 0Bit \;\simeq\; S^0, and used the occasion for the fun remark that in this sense the S nS^n are types of “higher homotopy bits”

    am making a corresponding edit also at 0-sphere

    diff, v21, current

  5. added section about the boolean domain’s rules with typal computation and uniqueness rules, and the corresponding dependent universal property of the boolean domain

    Anonymous

    diff, v23, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 24th 2023

    Not sure if it makes sense to duplicate the rules in this way, it seems confusing without comment. Maybe better to merge the two rule sets and add a comment below on the different posdibilities of equality in the computation rule.

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeMar 26th 2023

    adding a section about the extensionality principle for the boolean domain.

    diff, v26, current

  8. Added a sentence that the boolean domain is the tensor unit for the smash product in the monoidal category of pointed sets

    Joachim Joszef

    diff, v27, current

  9. undid last edit because it’s the singleton not the boolean domain which is the tensor unit for the smash product.

    Joachim Joszef

    diff, v27, current

    • CommentRowNumber10.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 6th 2023

    You were right the first time, Joachim.

    (Although I do find it an odd and overworked entry, stretching back to the earliest days.)

  11. Added back the sentence

    Joachim Joszef

    diff, v27, current

  12. Moved the sections on the “type of decidable propositions” and “type of booleans” from the type of propositions article over to this article

    diff, v29, current

  13. merging most of the contents of two-valued type into this article since it is referring to the same concept

    diff, v31, current

1 to 13 of 13

  1.