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 \(x\in S\).
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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