a1 Mathematics Department, Chung-Ang University, Seoul 151, Korea.
a2 Pure Mathematics Department, University of Sydney, New South Wales 2006, Australia.
An adjoint-triangle theorem contemplates functors P: C → A and T: A → B where T and TP have left adjoints, and gives sufficient conditions for P also to have a left adjoint. We are concerned with the case where T is conservative - that is, isomorphism-reflecting; then P has a left adjoint under various combinations of completeness or cocompleteness conditions on C and A, with no explicit condition on P itself. We list systematically the strongest results we know of in this direction, augmenting those in the literature by some new ones.
(Received August 25 1986)