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.