Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads
type: Item
instance of: scholarly article
title: Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads
zbMATH Open document ID: 0787.18007
DOI: 10.1007/BF00872987
author: Max Kelly
author: Stephen Lack
published in: Applied Categorical Structures
publication date: 1994-05-15T00:00:00Z
review text: The authors study the 2-monads on the 2-category CAT of small categories, which are completely determined, in the following sense, by their action on the finite discrete categories: the monad \(T\) is the left Kan extension of its restriction to the finite discrete categories. The authors investigate in particular the relations between this problem and the preservation of finite products by a left Kan extension.
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18D20
zbMATH DE Number: 458990
zbMATH Keywords: enriched categories
zbMATH Keywords: 2-monads
zbMATH Keywords: 2-category
zbMATH Keywords: products
zbMATH Keywords: Kan extension
zbMATH Keywords: monads
reviewed by: F. Borceux
MaRDI profile type: Publication
cites work: On product-preserving Kan extensions
cites work: A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on
cites work: Q3934579
cites work: Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads
description: scientific article; zbMATH DE number 458990