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

G. M. Kelly*, Stephen Lack

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


We study those 2-monads on the 2-category Cat 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.

Original languageEnglish
Pages (from-to)85-94
Number of pages10
JournalApplied Categorical Structures
Issue number1
Publication statusPublished - Mar 1993
Externally publishedYes


  • 2-monads
  • Categories with structure
  • finite-product-preserving functors
  • Kan extensions
  • Mathematics Subject Classifications (1991): 18C15, 18D20, 18A40


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