Let $A$ be a finite dimensional $K$-algebra ($K$ algebraic closed) and let $A$-mod denote the category of finitely generated modules over $A$.
It seems, (well, I do know) that $A$-mod is a hereditary category. You can read it In Remark 1.2(i) here. However, I have not been able to find a standard textbook with a proper proof or at least with an stattement of this fact. Dou you know of any?
I have looked at Atiyah-Donaldson, some papers about quiver representations and the books about categoyr theory I know: MacLane's Category theory, Awodey 2nd edition and Harold Simmons An Introduction to Category Theory. And also Cartan-Eilenberg Homological Algebra, but without any succes.
Thank you.