Dispersed Factorization Structures

Factorization structures on a category form a useful categorical tool. As is known, any , satisfying suitable completeness—and smallness—conditions, has a sufficient supply of factorization structures; in fact, there is a bijection between the class of all epireflective (full and isomorphism- closed) subcategories of and the class of all so called perfect factorizationstructures of In this paper, for an arbitrary category supplied with a fixed factorization structure (E, M), a similar bijection between the class of all E-reflective (full and isomorphism-closed) subcategories of and the class of all (E, M)-dispersed factorization structures on , introduced in this paper, will be established.