Finite posets

Here is some terminology used in this file:

  • An order filter (or upper set) of a poset \(P\) is a subset \(S\) of \(P\) such that if \(x \leq y\) and \(x\in S\) then \(y\in S\).
  • An order ideal (or lower set) of a poset \(P\) is a subset \(S\) of \(P\) such that if \(x \leq y\) and \(y\in S\) then \(x\in S\).
sage.categories.finite_posets.FinitePosets

The category of finite posets i.e. finite sets with a partial order structure.

EXAMPLES:

sage: FinitePosets()
Category of finite posets
sage: FinitePosets().super_categories()
[Category of posets, Category of finite sets]
sage: FinitePosets().example()
NotImplemented

See also

Posets, Poset()