k   field
A   finite dimensional k-algebra (associative, with 1, usually not semisimple).
n   number of simple (= irreducible) A-modules.

Modules are usually finitely generated left A-modules
mod A   the category of these A-modules (a length category: abelian, all objects have finite length)

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 progenerator iff P is finitely generated, projective, and a generator)
If P is a progenerator with B = End P,
    then Hom(P, - ) : mod A → mod B is an equivalence