Abstract:   Auslander's formula suggests that for studying an abelian category, one may study the category of finitely presented additive functors on it, that has nicer homological properties than the category itself, and then translate the results back to the original category. According to H. Lenzing, a considerable part of Auslander's work on the representation theory of finite dimensional, or more general artin, algebras can be connected to this formula.

In this talk, we first recall the Auslander's proof of the formula and then introduce and study a relative version of it. As application, some connections between the Morita equivalences of the endomorphism algebras of generators and the Morita equivalences of the original algebras will be provided.
The talk is based on a joint work with R. Hafezi and M. H. Keshavarz.