notifications

Order Theory

Wikipedia nLab

Preorder

Wikipedia nLaba ≤ a (reflexive),(a ≤ b) × (b ≤ c)(a ≤ c) (transitive).

Meet

nLabx ∧ y ≤ x, x ∧ y ≤ y,(a ≤ x) × (a ≤ y) → a ≤ x ∧ y.

Join

nLabx ≤ x ∨ y, y ≤ x ∨ y,(x ≤ a) × (y ≤ a) → x ∨ y ≤ a.

Partial Order

Wikipedia nLab(x ≤ y) × (y ≤ x) → x = y (antisymmetric).

Order

Lattice

Comparison with Cateogory Theory

nLab

References