On regular monomorphisms in weakly locally presentable categories (Q678842)

\textit{J. Adámek}, \textit{H. Hu} and the reviewer [J. Pure Appl. Algebra 107, No. 1, 1-8 (1996; Zbl 0852.18002)] showed that in a \(\kappa\)-accessible category \({\mathcal A}\) with pushouts, regular monomorphisms are closed under \(\kappa\)-directed colimits in \({\mathcal A}^2\) (the arrow category of \({\mathcal A})\), which implies that \(\kappa\)-pure morphisms of \({\mathcal A}\) must be regular monomorphisms. In the paper under review, the authors show that the same result can be established in a \(\kappa\)-accessible category \({\mathcal A}\) with products, thus solving an open problem formulated in the paper mentioned first.