Weak Factorization Systems and Topological Functors

Weak factorization systems, important in homotopy theory, are related to injective objects in comma{categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not coobrantly generated. We also present a weak factorization system on the category of posets which is not coobrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey.