  We extend \cite{G} to the nonsemisimple case. We define and study exact
factorizations $\B=\A\bullet \C$ of a finite tensor category $\B$ into a
product of two tensor subcategories $\A,\C\subset \B$, and relate exact
factorizations of finite tensor categories to exact sequences of finite tensor
categories with respect to exact module categories \cite{EG}. We apply our
results to study exact factorizations of quasi-Hopf algebras, and extensions of
a finite group scheme theoretical tensor category \cite{G2} by another one. We
also provide several examples to illustrate our results.

Quantum Algebra