NONSIKGULAR INJECTIVS MODULES 11
Proof. If F : 7?(S) - 7?(R) is a category equivalence, then
A = F(S) is a generator in 7?(R), and EndR(A) 2*Endg(S) s«S# By
1.17, A is faithful.
Conversely, suppose there is a faithful right R-module A e 7?(R)
such that EndR(A) a;S. Then A is a generator in ??(R) by 1.17.
Since 7?(R) is a spectral category (by 1.13), we conclude from
[3, Satz 2.l] that ??(R) is equivalent to 7?(S).