Manolo SaorĂn, Universidad de Murcia

TITLE: Special preenveloping torsion classes in general
abelian categories.

ABSTRACT.- It is well-known that in module categories the
torsion classes which are monomorphic special preenveloping are
precisely the ones given by a 1-tilting module. In this talk, we
will study torsion classes which are (not necessarly monomorphic)
special preenvoping in quite general abelian categories. We will see
that the relation with tilting theory in abelian categories, as
developed by members of the Algebra groups of Padova and
Verona, is still there, but there are differences. For
instance, not all tilting torsion classes need be special
preenveloping. The quite general context admits categorical
dualization, so that the precise relationship between special
precovering and cotilting torsionfree classes will be also
understood.