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


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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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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