n = n(A)		the number of simple (= irreducible) A-modules.
Any finite dimensional algebra has only finitely many simple A-modules, However, there may be infinitely many isomorphism classes of indecomposable A-modules.
mod A		denotes the category of (fin.dim.) A-modules
		(it is a length category: abelian, all objects have finite length)

Morita equivalence

Two algebras A, B are called Morita equivalent,
provided the categories mod A and mod B are equivalent,
thus provided there exists a progenerator in mod A with endomorphism ring B.
(P is a progenerator iff P is finitely generated, projective, and a generator.)
If the A-module P is a progenerator with B = End P,
then Hom_A(P, - ) : mod A → mod B is an equivalence.