[[Poset]]
# Preorder
A **preoder** 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

1. **reflexive** — for all $a \in S$, $(a,a) \in R$
2. **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 [[Preorders as categories]].

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