Distributive laws and factorization
type: Item
instance of: scholarly article
title: Distributive laws and factorization
zbMATH Open document ID: 1023.18002
DOI: 10.1016/S0022-4049(02)00140-8
published in: Journal of Pure and Applied Algebra
publication date: 2002-12-02T00:00:00Z
review text: \textit{M. Korostenski} and \textit{W. Tholen's} paper [ibid. 85, 57-72 (1993; Zbl 0778.18001)] has shown that factorization systems on categories are equivalent to normal pseudo-algebras for the 2-monad \((-)^{\mathbf{2}}\). This paper shows that distributive laws in the bicategory of set-valued matrices, strict factorization systems on categories, and strict algebras for the 2-monad on \({\mathcal C}{\mathcal A}{\mathcal T}\) given by \((-)^{\mathbf{2}}\) and the structure induced by the cocommutative comonoid \(\mathbf{1}\leftarrow \text\textbf{2}\leftarrow \text\textbf{2}\times \text\textbf{2}\) are equivalent.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 18D05
zbMATH DE Number: 1839073
zbMATH Keywords: distributive laws
zbMATH Keywords: strict factorization systems
zbMATH Keywords: strict algebras
author: Robert Rosebrugh
author: R. J. Wood
MaRDI profile type: Publication
cites work: Variation through enrichment
cites work: Q3961638
cites work: Weak subobjects and the epi-monic completion of a category.
cites work: Functorial factorization, well-pointedness and separability
cites work: Q4100671
cites work: Factorization systems as Eilenberg-Moore algebras
cites work: The formal theory of monads. II
cites work: Duality for groups
cites work: A basic distributive law
cites work: Q4888793
cites work: The formal theory of monads
cites work: Matched pairs of groups and bismash products of hopf algebras
cites work: Q3708172
full work available at URL: s0022-4049(02)00140-8
OpenAlex ID: W2037775432
description: scientific article; zbMATH DE number 1839073