RESUMO / ABSTRACT
October 1998
George Janelidze, Georgian Academy of Sciences (Tbilisi)
Semi-abelian categories
The well known notion of abelian category goes back essentially to S.Mac
Lane's famous paper "Duality for groups"; these categories provide an
abstract setting for the theory of (abelian groups and) modules. The
categories which the authors decided to call semiabelian similarly
generalize the varieties of groups (possibly with multiple operators, which
includes rings and algebras). The axioms for semiabelianess are not new: to
the contrary, we obtain a surprising theorem which in fact says that the
various old and new attempts to define such a notion do agree. Our results
once again show the power of two beautiful discovers: M.Barr's exactness
and D.Bourn's protomodularity.
