# πOrder

**Preorder** (proset) is a binary relation ($\leq$) that is reflexive and transitive. (Preorder is isomorphic to Thin Category.)

**Partial order** (poset) is a preorder s.t. $\forall x,y.\; x \leq y \land y \leq y \implies x = y$. i.e., reflexive, transitive, and antisymmetric.

**Total order** (linear order, loset) is like partial order, but with Connex property (i.e., defined between any two elements)

## Backlinks

- π Nominal subtyping establishes a partial order
- π Thin Category
- π Β§ Math