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nLab > Latest Changes: preorder

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2022

    In the section As a category, I have hyperlinked a couple of “Equivalently we may…” and “In other words we…” to the new entry relation between preorders and (0,1)-categories.

    diff, v62, current

    • CommentRowNumber2.
    • CommentAuthoramelia.liao
    • CommentTimeSep 18th 2022

    Fixed section on HoTT preorders/partial orders. The terminology in use before was incoherent and fairly inconsistent (e.g. using ∧ to stand for transitivity) and while preorders and equivalence relations are both symmetric and transitive, it detracts from the exposition on this page to smush them together. Preorders are more naturally generalised to partial orders.

    Added a paragraph explaining that partial orders in HoTT force the type they apply to be an h-set.

    diff, v63, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeJun 5th 2023

    moving Theorem 3.1 and its proof from specialization order to preorder because the proof applies to all binary relations, not just that of the membership relation between elements and open sets of a topological space.

    diff, v66, current

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 5th 2023

    Added buzzwords “codensity monad” and “guarded quantification” to the beginning of the section on deriving a preorder from a predicate.

    diff, v67, current

1 to 4 of 4

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