 In order to overcome the limitations of the original method of fibring as exposed in the last subsection, A. Sernadas and collaborators propose, in Sernadas et al. 1999, a general definition of fibring using the conceptual tools of category theory. The central idea of the generalization is simple: suppose that \({{\cal L}}_1\) and \({{\cal L}}_2\) are two propositional logics which are to be combined. Suppose, for simplicity, that no connectives are to be shared, that is, the language of the logic \({{\cal L}}\) to be obtained is the free combination of the connectives of both logics. In categorial terms, the signature \(C\) of \({{\cal L}}\) is the coproduct (disjoint union) of the signatures \(C_1\) of \({{\cal L}}_1\) and \(C_2\) of \({{\cal L}}_2\), in the underlying category of signatures. Then \({{\cal L}}\), which is the least logic defined over \(C\) which extends simultaneously \({{\cal L}}_1\) and \({{\cal L}}_2\), is defined as the coproduct of \({{\cal L}}_1\) and \({{\cal L}}_2\) in the underlying category of logics. The minimality of \({{\cal L}}\) attends a criterion expressed in Gabbay 1999 (see also  section 5)  and also conforms to the ideal of fusing logics, see Kracht and Wolter 1991. This combination process, called unconstrained fibring, can be generalized, by allowing \(C_1\) and \(C_2\) to share some connectives. Thus, the logic obtained by this second kind of fibring is defined in a language such that some connectives of \({{\cal L}}_1\) and \({{\cal L}}_2\) are identified. The logic produced by this operation, called constrained fibring, starts by considering two logics \({{\cal L}}_1\) and \({{\cal L}}_2\) over signatures \(C_1\) and \(C_2\), respectively, and a signature \(C_0\) contained in both \(C_1\) and \(C_2\). This signature contains exactly the connectives of \({{\cal L}}_1\) and \({{\cal L}}_2\) which are to be identified (or shared) throughout the combination process. After computing the unconstrained fibring (that is, the coproduct) \({{\cal L}}_1 \oplus {{\cal L}}_2\) of \({{\cal L}}_1\) and \({{\cal L}}_2\), which is defined over the signature \(C_1 \oplus C_2\) (the coproduct of \(C_1\) and \(C_2\)), a new logic \({{\cal L}}\) is obtained. This logic, the fibring of \({{\cal L}}_1\) and \({{\cal L}}_2\) by sharing (or constrained to) \(C_0\), is obtained from \({{\cal L}}_1 \oplus {{\cal L}}_2\) by identifying two connectives (of the same arity) iff both come from the same connective in \(C_0\). In terms of category theory, it is required that the forgetful functor \(N\) from the category of logics to the category of signatures be a cofibration. Then, if \(i_j:{{\cal C}}_0\to C_j\) is the inclusion morphism (for \(j=1,2\)), \(h_j:C_j \to C_1 \oplus C_2\) is the canonical injection of the coproduct (for \(j=1,2\)) and \(q:C_1 \oplus C_2 \to C\) is the coequalizer of \(h_1 \circ i_1\) and \(h_2 \circ i_2\), then the constrained fibring \({{\cal L}}\) is the codomain of the cocartesian lifting of \(q\) by \(N\).