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Density presentations of functors

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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Abstract

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The article contains the basic theory resulting from the presentation of a dense functor N: A → C by means of an expansion K(k, C) ० NJk ≅ C the term dense functor being used instead of the equivalent term left-adequate functor. Results by various authors on the density type of a functor are formulated in the V-context for V symmetric monoidal closed, and elementary proofs are given. In particular a characterisation theorem containing the well-known results of Beck and Ulmer is established.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 427 - 448
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Appelgate, H. and Tierney, M., “Categories with models”, Seminar on triples and categorical homology theory, 156–244 (Lecture Notes in Mathematics, 80. Springer-Verlag, Berlin, Heidelberg, New York, 1969).CrossRefGoogle Scholar
[2]Barr, Michael, “Coequalisers and free triples”, Math. Z. 116 (1970), 307–322.CrossRefGoogle Scholar
[3]Barr, Michael, “Exact categories”, Exact categories and categories of sheaves, 1–120 (Lecture Notes in Mathematics, 236. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[4]Borceux, Francis and Day, Brian, “Universal algebra in a closed category”, J. Pure Appl. Algebra (to appear).Google Scholar
[5]Borceux, Francis and Kelly, G.M., “A notion of limit for enriched categories”, Bull. Austral. Math. Soc. 12 (1975), 49–72.CrossRefGoogle Scholar
[6]Bunge, Marta C., “Relative functor categories and categories of algebras”, J. Algebra 11 (1969), 64–101.CrossRefGoogle Scholar
[7]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
[8]Day, B.J., “Varieties of a closed category”, Bull. Austral. Math. Soc. 16 (1977), 131–145.CrossRefGoogle Scholar
[9]Diers, Yves, “J-adjonction, limite J-absolue et J-théorie algêbrique”, C.R. Acad. Sci. Paris Sér. A 278 (1974), 1009–1012.Google Scholar
[10]Diers, Yves, “Type de densité d'une sous-catégorie pleine”, Ann. Soc. Sci. Bruxelles Sér. I 90 (1976), 25–47.Google Scholar
[11]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).Google Scholar
[12]Freyd, P.J. and Kelly, G.M., “Categories of continuous functors, I” Pure Appl. Algebra 2 (1972), 169–191.CrossRefGoogle Scholar
[13]Gabriel, Peter, Ulmer, Friedrich, Lokal präsentierbare Kategorien (Lecture Notes in Mathematics, 221. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[14]Gildenhuys, Dion and Lim, Chong-Keang, “Free pro-C-groups”, Math. Z. 125 (1972), 233–254.CrossRefGoogle Scholar
[15]Hofmann, Karl Heinrich, “Category theoretical methods in topological algebra”, Categorical topology, 345–403 (Proc. Conf. Mannheim, 1975. Lecture Notes in Mathematics, 540. Springer-Verlag, Berlin, Heidelberg, New York, 1976).CrossRefGoogle Scholar
[16]Isbell, J.R., “Adequate subcategories”, Illinois J. Math. 4 (1960), 541–552.CrossRefGoogle Scholar
[17]Kennison, J.F. and Gildenhuys, Dion, “Equational completions, model induced triples and pro-objects”, J. Pure Appl. Algebra 1 (1971), 317–346.CrossRefGoogle Scholar
[18]Lawvere, F. William, “Metric spaces, generalized logic, and closed categories”, Lecture Notes, istituto di Matematica, Università di Perugia.Google Scholar
[19]Chong-Keang, Lim, “Tripleableness of pro-C-groups”, J. Austral. Math. Soc. Ser. A 21 (1976), 299–309.CrossRefGoogle Scholar
[20]Linton, F.E.J., “Some aspects of equational categories”, Proc. Conf. Categorical Algebra, La Jolla, California, 1905, 84–94 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[21]Lane, S. Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, New York, Heidelberg, Berlin, 1971).CrossRefGoogle Scholar
[22]Ulmer, Friedrich, “Properties of dense and relative adjoint functors”, J. Algebra 8 (1968), 77–95.CrossRefGoogle Scholar