Tilting theory

Summary

Tilting theory compares the module categories of two algebras $A$ and $B = \End_A(T)$ by means of a tilting module $T$. It generalizes Morita equivalence, which is the case where $T$ is a progenerator. The two module categories are not equivalent in general, but they share large pieces, and by Happel's theorem their bounded derived categories are equivalent. It grew out of the reflection functors of Bernstein, Gelfand and Ponomarev.