Subject: categories: flat covers

From: Jiri Rosicky <[email-masked]>
Date: Wed, 9 Feb 2000 14:08:06 +0100 (CET)

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