Extensions of MV, BCI and BCK-algebras (Q1326521)

We consider various categories \({\mathbf C}\) of BCI, BCK or MV-algebras. It is shown that these categories are complete. Extensions of one algebra by another in \({\mathbf C}\) are then defined and an equivalence relation is set up. It is shown that the set of equivalence classes of extensions by a fixed algebra in \({\mathbf C}\) gives rise to a contravariant functor \({\mathbf C}\to \text{Sets}\).