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Linear monads

Published online by Cambridge University Press:  17 April 2009

B. J. Day
B. J. Day
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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A monad T = (T, μ, η) on a category C is said to be linear with respect to a dense functor N: A → C if the operator T is the epimorphic image of a certain colimit of its values on A. The main aim of the article is to relate the concept of a linear monad to that of a monad with rank. A comparison is then made between linear monads and algebraic theories.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 2 , October 1977 , pp. 177 - 192
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Borceux, Francis and Day, Brian, “Universal algebra in a closed category”, J. Pure Appl. Algebra (to appear).Google Scholar
[2]Day, Brian, “On closed categories of functors II”, Category seminar, 20–54 (Proc. Sydney Category Seminar 1972/1973. Lecture Notes in Mathematics, 420.Springer-Verlag,Berlin, Heidelberg, New York,1974).CrossRefGoogle Scholar
[3]Day, B.J., “Density presentations of functors”, Bull. Austral. Math. Soc. 16 (1977), 427–448.CrossRefGoogle Scholar
[4]Day, B.J. and Kelly, G.M., “Enriched functor categories”, Report of the Midwest Category Seminar III, 178–191 (Lecture Notes in Mathematics, 106. Springer-Verlag, Berlin, Heidelberg, New York, 1969).CrossRefGoogle Scholar
[5]Diers, Y., “Foncteur pleinement fidèle dense classant les algèbres”, (Publications Internes de l'U.E.R. de Mathématiques Pures et Appliquées, 58. Université des Science et Techniques de Lille I, 1975).Google Scholar
[6]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
[7]Freyd, P.J. and Kelly, G.M., “Categories of continuous functors, I”, J. Pure Appl. Algebra 2 (1972), 169–191.CrossRefGoogle Scholar
[8]Linton, F.E.J., “Coequalisers in categories of algebras”, Seminar on Triples and Categorical Homology Theory, 75–90 (Lecture Notes in Mathematics, 80. Springer-Verlag, Berlin, Heidelberg, New York, 1969).CrossRefGoogle Scholar
[9]Lane, S. Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, New York, Heidelberg, Berlin, 1971).CrossRefGoogle Scholar