Nakayama functors and Eilenberg–Watts theorems

In the present paper analogues of Eilenberg–Watts theorem are proved for categories of finitely generated modules over finite dimensional algebras for right exact and left exact functors. Furthermore, for left exact functors corresponding bimodules are described explicitly. The main aim of this paper is to present how one can obtain some new descriptions of Nakayama functor and inverse Nakayama functor for selfinjective algebras with this versions of Eilenberg–Watts theorem.