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Adjoint-triangle theorems for conservative functors

  • G. B. Im (a1) and G. M. Kelly (a2)
Abstract

An adjoint-triangle theorem contemplates functors P: CA and T: AB 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.

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References
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[1]Dubuc, E., “Adjoint triangles”, Lecture Notes in Math. 61 (1968), 6991.
[2]Huq, S.A., “An interpolation theorem for adjoint functors”, Proc. Amer. Math. Soc. 25 (1970), 880883.
[3]Im, G.B. and Kelly, G.M., “Some remarks on conservative functors with left adjoints”, J. Korean Math. Soc. 23 (1986), 1933.
[4]Kelly, G.M., “Monomorphisms, epimorphisms, and pullbacks”, J. Austral. Math. Soc. 9 (1969), 124142.
[5]Kelly, G.M., Basic Concepts of Enriched Category Theory, (London Math. Soc. Lecture Notes Series 64, Cambridge University Press, 1982).
[6]Kelly, G.M., “A survey of totality for enriched and ordinary categories”, Cahiers Topologie Géom. Différentielle, 27 (1986), 109132.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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