Page "Isomorphism of categories" Paragraph 11

Conversely, given a left kG module M, then M is a k vector space, and multiplication with an element g of G yields a k-linear automorphism of M ( since g is invertible in kG ), which describes a group homomorphism G → GL ( M ).

( There are still several things to check: both these assignments are functors, i. e. they can be applied to maps between group representations resp.

kG modules, and they are inverse to each other, both on objects and on morphisms ).