Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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.