flat covers

The flat cover conjecture was formulated by E. Enochs in 1981 and asks whether every module has a flat cover. In his paper, he also showed that it is equivalent to weak coreflectivity of flat modules in modules. In 1995, J. Xu has proved that it is true over commutative noetherian rings of finite Krull dimension. The flat cover conjecture has been recently proved (over an arbitrary ring) by L. Bican, R. El Bashir and E. Enochs. In a paper "Flat covers and factorizations", I am giving a purely categorical proof based on the theorem of J. Smith about weak factorization systems. Jiri Rosicky