Kazama–Suzuki coset construction and its inverse

We study the representation theory of Kazama-Suzuki coset vertex operator superalgebra associated with pair a complex simple Lie algebra and its Cartan subalgebra. In case type $A_{1}$, B.L. Feigin, A.M. Semikhatov, I.Yu. Tipunin introduced another construction, which is "inverse" construction. this paper we generalize latter construction to arbitrary establish categorical equivalence between categories certain modules over an affine corresponding superalgebra. Moreover, when regular, prove that also regular category ordinary carries braided monoidal structure by tensor categories.