Poset

Preorder

A preoder is a Poset without the property of antisymmetry, order i.e. a set equipped with a relation 𝑅 such that 𝑅 (viewed here as a set) is

  1. reflexive β€” for all π‘Ž βˆˆπ‘†, (π‘Ž,π‘Ž) βˆˆπ‘…
  2. transitive β€” if (π‘Ž,𝑏) βˆˆπ‘… and (𝑏,𝑐) βˆˆπ‘…, then (π‘Ž,𝑐) βˆˆπ‘…

A preorder is equivalent to a Thin category, see Preorders as categories.


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