Abstract
This chapter describes the perfect projectors and perfect injectors. It is assumed that R and S are rings and Rm and Sm are the categories of all left R-modules and left S-modules, respectively. An (R, S) adjoint triple is a triple of additive functors. It is shown that a triple of functors (G, F, H) is an (R, S) adjoint triple if there is bimodule gPR with PR finitely generated and projective such that F, G, H are naturally equivalent to the functors. It is found that when Fp is an equivalence, it preserves all categorical properties. In the more general setting, much of the structure may be lost in passing from Rm to Sm through Fp. An epimorphism f: B → D is minimal if for any homomorphism g : B′ → B; if g0f is an epimorphism, then g is an epimorphism.
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