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On characterisation of finitary algebraic categories

Published online by Cambridge University Press:  17 April 2009

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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Abstract

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The aim of this article is to characterise categories which are V–algebraic (equals V–theoretical) over V where V is a symmetric monoidal closed category satisfying suitable limit-colimit commutativity conditions (basicly axiom π).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Beck, Jon, “On H–spaces and infinite loop spaces”, Category theory, homology theory and their applications III, 139153 (Proc. Conf. Seattle Research Center, Battelle Memorial Institute, 1968, Volume Three. Lecture Notes in Mathematics, 99. Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[2]Boardman, J.M. and Vogt, R.M., “Homotopy–everything H–spaces”, Bull. Amer. Math. Soc. 74 (1968), 11171122.CrossRefGoogle Scholar
[3]Borceux, Francis and Day, B.J., “On product-preserving Kan extensions”, Bull. Austral. Math. Soc. 17 (1977), 247255.CrossRefGoogle Scholar
[4]Borceux, Francis and Day, Brian, “Universal algebra in a closed category”, J. Pure Appl. Algebra (to appear).Google Scholar
[5]Day, B.J., “Linear monads”, Bull. Austral. Math. Soc. 17 (1977), 177192.CrossRefGoogle Scholar
[6]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
[7]Diers, Yves, “Type de densité d'une sous–catégorie pleine”, Ann. Soc. Sci. Bruxelles Sér. I 90 (1976), 2547.Google Scholar
[8]lenberg, Samuel Ei and Kelly, G. Max, “Closed categories”, Proc. Conf. Categorical Algebra, La Jolla, California, 1965, 421562 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[9]Kelly, G.M., “On the operads of J.P. May”, unpublished manuscript.Google Scholar
[10]Lane, S. Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[11]May, J.P., The geometry of iterated loop spaces (Lecture Notes in Mathematics, 271. Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar