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Applied Categorical Structures

, Volume 1, Issue 1, pp 85–94 | Cite as

Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads

  • G. M. Kelly
  • Stephen Lack
Article

Abstract

We study those 2-monads on the 2-categoryCat of categories which, as endofunctors, are the left Kan extensions of their restrictions to the sub-2-category of finite discrete categories, describing their algebras syntactically. Showing that endofunctors of this kind are closed under composition involves a lemma on left Kan extensions along a coproduct-preserving functor in the context of cartesian closed categories, which is closely related to an earlier result of Borceux and Day.

Mathematics Subject Classifications (1991)

18C15 18D20 18A40 

Key words

Categories with structure 2-monads finite-product-preserving functors Kan extensions 

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References

  1. 1.
    F. Borceux and B.J. Day: 1977, ‘On product-preserving Kan extensions’,Bull. Austral. Math. Soc. 17, 247–255.Google Scholar
  2. 2.
    B.J. Day: 1970, ‘Construction of biclosed categories’, Ph.D. Thesis, University of New South Wales.Google Scholar
  3. 3.
    G.M. Kelly: 1980, ‘A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on’,Bull. Austral. Mat. Soc. 22, 1–83.Google Scholar
  4. 4.
    G.M. Kelly: 1982,Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Notes Series 64, Cambridge Univ. Press.Google Scholar
  5. 5.
    G.M. Kelly: 1982, ‘Structures defined by finite limits in the enriched context I’,Cahiers de Topologie et Géometrie Différentielle 23, 3–42.Google Scholar
  6. 6.
    G.M. Kelly and A.J. Power: ‘Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads’,J. Pure Appl. Algebra, to appear.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • G. M. Kelly
    • 1
  • Stephen Lack
    • 1
  1. 1.School of Mathematics and Statistics F07University of SydneyAustralia

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