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Adjoint-triangle theorems for conservative functors

Published online by Cambridge University Press:  17 April 2009

G. B. Im  and
G. M. Kelly
G. B. Im
Affiliation:
Mathematics Department, Chung-Ang University, Seoul 151, Korea.
G. M. Kelly
Affiliation:
Pure Mathematics Department, University of Sydney, New South Wales 2006, Australia.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 133 - 136
Copyright
Copyright © Australian Mathematical Society 1987

References

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