Flows with respect to a functor (Q1840757)

Generalizing earlier work on factorizations of cones and cocones along a functor [see \textit{W. Tholen}, Quaest Math. 2, 335-353 (1977; Zbl 0365.18003)] and, more recently, of so-called flows in a category [see \textit{H. Herrlich} and \textit{W. Meyer}, Quaest. Math. 17, No. 1, 1-11 (1994; Zbl 0810.18002)], the author studies \(F\)-structured factorizations of families of morphisms \(f_{ij}:FA_i\to B_j\) \((i\in I, j\in J)\), where \(I\) is a class, \(J\) a set, and \(F\) a given functor.