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
TESTS:
sage: C = LatticePosets()
sage: TestSuite(C).run()
alias of FiniteLatticePosets
Returns the join of and
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
Returns the meet of and
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
Returns a list of the (immediate) super categories of self, as per Category.super_categories().
EXAMPLES:
sage: LatticePosets().super_categories()
[Category of posets]