Lax orthogonal factorisation systems (Q317326)

The paper introduces lax orthogonal algebraic weak factorization systems on \(2\)-categories. They extend the usual factorization systems on categories and their definition is motivated by algebraic weak factorization systems on categories. There is shown how to construct them from simple \(2\)-monads generalizing simple reflections of categories (see Zbl [\textit{C. Cassidy} et al., J. Aust. Math. Soc., Ser. A 38, 287--329 (1985; Zbl 0573.18002)]). For example, these monads arise from completions of categories under a class of colimits.