Preorder

A proset is a poset without the property of antisymmetry, #m/def/order i.e. a set equipped with a relation $𝑅$ such that $𝑅$ (viewed here as a set) is

reflexive — for all $𝑎 \in 𝑆$ , $(𝑎, 𝑎) \in 𝑅$
transitive — if $(𝑎, 𝑏) \in 𝑅$ and $(𝑏, 𝑐) \in 𝑅$ , then $(𝑎, 𝑐) \in 𝑅$

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

#state/tidy | #lang/en | #SemBr