Pre-Order

Definition

A preorder is a relation $R:A\to A\to \mathrm{Prop}$ s.t.

• $R$ is Reflexive Relation
• $R$ is transitive

Remarks

Every pre-order forms a Thin Category.

Duplicate Content 1

A relation $\sim :A\text{texttimes}A\to \mathrm{Prop}$ is a pre-order iff

• it is reflexive, and Transitive Relation