Name for concept: each pair of sets is either nested or disjoint Does this property have a name?


  Given a collection of sets $\mathcal{P}$, for   all pairs $A, B\in\mathcal{P}$, either $A\cap B=\emptyset$ or $A\subseteq B$ or $B\subseteq A$.


This concept could equally apply to monoids, groups, partial orders or other mathematical structures, with some adjustments to the definitions. For instance, for monoids and groups we would replace $A\cap B=\emptyset$ by $A\cap B=\{\epsilon\}$, where $\epsilon$ is the unit of the monoid/group.
I think that's called a laminar family.