Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T23:59:05.240Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Dubuc, E., “Adjoint triangles”, Lecture Notes in Math. 61 (1968), 69–91.CrossRefGoogle Scholar
[2]Huq, S.A., “An interpolation theorem for adjoint functors”, Proc. Amer. Math. Soc. 25 (1970), 880–883.CrossRefGoogle Scholar
[3]Im, G.B. and Kelly, G.M., “Some remarks on conservative functors with left adjoints”, J. Korean Math. Soc. 23 (1986), 19–33.Google Scholar
[4]Kelly, G.M., “Monomorphisms, epimorphisms, and pullbacks”, J. Austral. Math. Soc. 9 (1969), 124–142.CrossRefGoogle Scholar
[5]Kelly, G.M., Basic Concepts of Enriched Category Theory, (London Math. Soc. Lecture Notes Series 64, Cambridge University Press, 1982).Google Scholar
[6]Kelly, G.M., “A survey of totality for enriched and ordinary categories”, Cahiers Topologie Géom. Différentielle, 27 (1986), 109–132.Google Scholar