# ct.category theory – What is the largest subcategory C of a module category over an Artin algebra, such that C is Krull-Schmidt (and albelian)? Does C exist?

Let $$A$$ be an Artin algebra, $$text{Mod},A$$ the category of $$A$$-modules and $$text{mod},A$$ the category of finitely generated $$A$$-modules. It is well-known that $$text{mod},A$$ is a Krull-Schmidt category. Can we find a larger full subcategory $$mathcal{C}$$ of $$text{Mod},A$$, such that it remains a Krull-Schmidt category? Is there a largest $$mathcal{C}$$ and if yes, how does $$mathcal{C}$$ look like? What happens if we additionally demand $$mathcal{C}$$ to be an albelian category?