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  1. two-valued objects are topos-theoretic analogues of the set 2\mathbf{2} with two elements in SetSet, and the categorical semantics of the type of booleans. Different from subobject classifiers. Still to do: categorical semantics of binary coproduct types and binary product types using dependent sums and products and two-valued objects.


    v1, current

  2. Added a few examples


    v1, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeMar 21st 2021
    A distinction ought to be made in the article between the two-valued object as the initial object with two points as defined in the definitions section, and two-valued objects as objects with two points and possibly additional structure. Properly speaking, a subobject classifier has the additional structure of a Heyting algebra or classically a Boolean algebra, and so cannot be the initial object with two points.
  3. Better definition to actually express initiality


    v1, current

  4. Reverted definition as the new definition is just an interval object.


    diff, v2, current

  5. Moving examples section to bi-pointed object


    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 6th 2023

    Tagging this as one of many articles of dubious quality.

  6. Considering that this article was created two years ago around the same time as two-valued type by some anonymous editor, and the two-valued type article essentially has the same content as boolean domain, wouldn’t a better name for the concept expressed in this article be “booleans object” or “boolean domain object” or some variation on that?

    Personally I’ve never seen “two-valued type” used for the type in type theory, nor “two-valued object” used for internalizing in a category, outside the nLab. Booleans or boolean domain is standard terminology for the type in type theory.

  7. renaming page to “boolean domain object” since it represents the concept of boolean domain internal to a category

    diff, v5, current