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On product-preserving Kan extensions

  • Francis Borceux (a1) and B. J. Day (a2)

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In this article we examine the problem of when a left Kan extension of a finite-product-preserving functor is finite-product preserving. This extension property is of significance in the development of finitary universal algebra in a closed category, details of which will appear elsewher. We give a list of closed categories with the required extension property.

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Copyright

COPYRIGHT: © Australian Mathematical Society 1977

References

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[1]Borceux, Francis and Day, Brian, “Universal algebra in a closed category”, J. Pure Appl. Algebra (to appear).
[2]Borceux, Francis and Kelly, G.M., “A notion of limit for enriched categories”, Bull. Austral. Math. Soc. 12 (1975), 49–72.
[3]Day, Brian, “On closed categories of functors”, Reports of the midwest Category Seminar IV, 1–38 (Lecture Notes in Mathematics, 137. Springer-Verlag, Berlin, Heidelberg, New York, 1970).
[4]Day, B.J. and Kelly, G.M., “Enriched functor categories”, Reports of the Midwest Category Seminar III, 178–191 (Lecture Notes in Mathematics, 106. Springer-Verlag, Berlin, Heidelberg, New York, 1969).
[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).
[6]Kelly, G.M., “Adjunction for enriched categories”, Reports of the Midwest Category Seminar III, 166–177 (Lecture Notes in Mathematics, 106. Springer-Verlag, Berlin, Heidelberg, New York, 1969).
[7]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).
[8]Lane, S. Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, New York, Heidelberg, Berlin, 1971).
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  • Cited by 7

  • Access

On product-preserving Kan extensions

  • Francis Borceux (a1) and B. J. Day (a2)

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