For finite abelian categories (category of modules over a finite dimensional algebra), Auslander proves a bijection between the following two classes: finite abelian categories that have only finitely many indecomposables (finite-type), and finite abelian categories that satisfy a “nice” homological property (gl.proj.dim <= 2 <= dom.dim). This correspondence, nowadays known as the Auslander correspondence, is essentially a consequence of the Yoneda embedding. In this talk, I will discuss an equivariant version of the Auslander correspondence. In this setting, finite abelian categories are equipped with actions of tensor categories, hence have well-defined internal Hom — the equivariant Auslander correspondence will therefore be a consequence of the internal Yoneda embedding instead. This is based on an ongoing joint work with Kevin Coulembier.