Distributive laws and factorization
\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.
scientific article; zbMATH DE number 1839073