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    • CommentRowNumber1.
    • CommentAuthorJohn Baez
    • CommentTimeMar 10th 2019

    Described the free suplattice on a poset.

    diff, v14, current

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 2nd 2019

    Added more information on the category SupLatSupLat.

    diff, v17, current

  1. The category of free suplattices is equivalent to Rel.

    diff, v19, current

  2. To what would Prof be analogously equivalent?

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 4th 2020
    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJun 4th 2020

    Wouldn’t it be presheaf categories, i.e. free cocomplete categories?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 4th 2020

    Oh, sorry, yes, I was reading much too quickly.

  3. added “finite” in definition to avoid misunderstanding.

    diff, v20, current

    • CommentRowNumber9.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 29th 2020

    Daniel, I’m sorry, but that’s just wrong. I’m going to have to revert.

    Normally I refer to posets with finite joins as a join-semilattice.

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 30th 2020

    Added “arbitrary subsets” to disambiguate.

    diff, v22, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2020

    I have touched the formatting:

    added a table of contents, moved the reference item to a References-section and provided it with hyperlinked ISBN. Also added hyperlinks to more of the technical terms.

    diff, v23, current

    • CommentRowNumber12.
    • CommentAuthorCatawampus
    • CommentTimeMay 28th 2024
    Re. the statement "To give a downset is to give an antichain,...", isn't this not true in general? I'm assuming what is meant is that taking the set of maximal elements of a downset defines a bijection between downsets and antichains, but that seems to not necessarily hold if the poset doesn't satisfy the ascending chain condition. E.g. in the natural numbers ordered by divisibility, {powers of 2} and {powers of 3} are both downsets with no maximal elements.
    • CommentRowNumber13.
    • CommentAuthorRodMcGuire
    • CommentTimeMay 29th 2024

    in the natural numbers ordered by divisibility, {powers of 2} and {powers of 3} are both downsets with no maximal elements.

    in the divisibility lattice, 00 is the maximal element of everything. If we say it is a power of 22, 0=2 0 = 2^\infty there is no downset that just contains powers of 22.

    This strikes me as a rather unsatisfactory fix.