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# Lattice posets

class `sage.categories.lattice_posets.``LatticePosets`(s=None)

  Bases: `sage.categories.category.Category`

  The category of lattices, i.e. partially ordered sets in which any two elements have a unique supremum (the elements’ least upper bound; called their join) and a unique infimum (greatest lower bound; called their meet).

  EXAMPLES:

      sage: LatticePosets()
      Category of lattice posets
      sage: LatticePosets().super_categories()
      [Category of posets]
      sage: LatticePosets().example()
      NotImplemented

  See also

  `Posets`, `FiniteLatticePosets`, `LatticePoset()`

  TESTS:

      sage: C = LatticePosets()
      sage: TestSuite(C).run()

  `Finite`

    alias of `FiniteLatticePosets`

  class `ParentMethods`
    `join`(x, y)

      Returns the join of \(x\) and \(y\) in this lattice

      INPUT:

      > - `x`, `y` – elements of `self`

      EXAMPLES:

          sage: D = LatticePoset((divisors(60), attrcall("divides")))
          sage: D.join( D(6), D(10) )
          30

    `meet`(x, y)

      Returns the meet of \(x\) and \(y\) in this lattice

      INPUT:

      > - `x`, `y` – elements of `self`

      EXAMPLES:

          sage: D = LatticePoset((divisors(30), attrcall("divides")))
          sage: D.meet( D(6), D(15) )
          3

  `LatticePosets.``super_categories`()

    Returns a list of the (immediate) super categories of `self`, as per `Category.super_categories()`.

    EXAMPLES:

        sage: LatticePosets().super_categories()
        [Category of posets]

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