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A monadicity theorem

Published online by Cambridge University Press:  17 April 2009

Francis Borceux  and
B. J. Day
Francis Borceux
Affiliation:
Institut de Mathématique pure et appliquée, Université Catholique de Louvain, Belgium;
B. J. Day
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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A monadicity theorem is established, for functors which satisfy the conditions of the “first isomorphism theorem” (following Linton's terminology). An application is made to the characterisation of certain types of algebraic categories generated by linear monads.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 2 , October 1977 , pp. 291 - 296
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Borceux, Francis and Kelly, G.M., “A notion of limit for enriched categories”, Bull. Austral. Math. Soc. 12 (1975), 49–72.CrossRefGoogle Scholar
[2]Day, B.J., “Linear monads”, Bull. Austral. Math. Soc. 17 (1977), 177–192.CrossRefGoogle Scholar
[3]Day, B.J., “On the rank of free monads” (Preprint, Department of Pure Mathematics, University of Sydney, Sydney, 1977).Google Scholar
[4]Diers, Y., “Foncteur pleinement fidèle dense classant les algèbres”, (Publications Internes de l'U.E.R. de Mathématiques Pures et Appliquées, 58. Université des Sciences et Techniques de Lille I, 1975).Google Scholar
[5]Eilenberg, Samuel and Kelly, G. Max, “Closed categories”,Proc. Conf. Categorical Algebra,La Jolla, California,1965,421–562 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[6]Linton, F.E.J., “Some aspects of equational categories”,Proc. Conf. Categorical Algebra,La Jolla, California,1965,84–94 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[7]Lane, S. Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar