The size of a stratifying system can be arbitrarily large

Abstract

In this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consists on stratifying systems of infinite size in the module category of an algebra $A$. In the second family of examples we show that the size of a finite stratifying system in the module category of a finite dimensional algebra $A$ can be arbitrarily large in comparison to the number of isomorphism classes of simple $A$-modules. We note that both families of examples are built using well-established results in higher homological algebra.

This version has been accepted for publication in \emph{Comptes Rendus Mathématique}. A simpler example of stratifying system of infinite size is given, leading to a more direct proof