The Brenner-Butler Theorem
Let T be a tilting A-module, B = End(T).
The categories
G
and
Y
are equivalent;
the categories
F
and
X
are equivalent.
An equivalence
G
→
Y
is given by the functor Hom
A
(T, - ).
An equivalence
F
→
X
is given by the functor Ext
1
(T, - ).