---
tag: TZWMEM7GKA
kind: concept
name: Disjoint union of posets
msc: [06A06]
sources:
  - url: https://en.wikipedia.org/wiki/Disjoint_union
---

## Summary

The disjoint union of partially ordered sets places them side by side, with no relation between elements of different parts.
Inside each part the order is unchanged.
It is also called the parallel composition, or cardinal sum, and it is the coproduct of posets.

## Explanations

### L1 human

Put two Hasse diagrams next to each other on the same page, without drawing any new lines.
That picture is the disjoint union.
Two separate two-element chains $a < b$ and $c < d$ give a poset with four elements in which $a$ and $d$ are incomparable.