In this paper the categories Mcon and Seq of multiple-conclusion consequence
relations and sequent calculi, respectively, are introduced. The main feature
of these categories is the preservation, by morphisms, of meta-properties
of the consequence relations. This feature is obtained by changing the usual
concept of morphism between logics (that is, a signature morphism preserving
deductions) by a stronger one (a signature morphism preserving meta-implications
between deductions). This allow us to obtain better results by fibring objects
in Mcon and in Seq than using the usual notion of morphism
between deduction systems: In fact, meta-fibring (that is, fibring in the
proposed categories) avoids the phenomenon of fibring that we call anti-collapsing problem, as opposite
to the well-known collapsing problem
of fibring. Additionally, a general semantics for objects in Seq (and, in particular, for objects in
Mcon) is proposed, obtaining
a category of logic systems called Log.
A general theorem of preservation of completeness by fibring in Log is also obtained.