Lax factorization algebras
In a factorization system for a category there are two classes of morphisms each class determining the other by a diagonal fill-in condition; the fill-in morphism is required to be unique. In homotopy theory, explicitly in Quillen model categories, the same thing happens without uniqueness: weak factorization systems. As what might be considered a follow-up to the realization that factorization systems can be regarded as Eilenberg-Moore algebras for a suitable monad [see \textit{M. Korostenski} and \textit{W. Tholen}, J. Pure Appl. Algebra 85, No.~1, 57-72 (1993; Zbl 0778.18001)], this paper compares lax algebras for the monad with weak factorization systems.
scientific article; zbMATH DE number 1839074