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


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.

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The first author gratefully acknowledges the support of the Australian Research Council.

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Kelly, G.M., Lack, S. Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads. Appl Categor Struct 1, 85–94 (1993). https://doi.org/10.1007/BF00872987

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Mathematics Subject Classifications (1991)

  • 18C15
  • 18D20
  • 18A40

Key words

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