Some categorical aspects of BCH-algebras

We show that the category BCH of BCH-algebras and BCH-homomorphisms is complete. We also show that it has coequalizers, kernel pairs, and an image factorization system. It is also proved that onto homomorphisms and coequalizers, and monomorphisms and one-to-one homomorphisms coincide, respectively, in BCH. It is shown that MBCI is a coreflexive subcategory of BCH. Regular homomorphisms have been defined and their properties are studied. An open problem has been posed

On some classes of BCH-algebras

The concept of a BCH-algebra is a generalization of the concept of a BCI-algebra. It is shown that weakly commutative BCH-algebras are weakly commutative BCI-algebras. Moreover, the concepts of weakly positive implicative and weakly implicative BCH-algebras are defined and it is shown that every weakly implicative BCH-algebra is a weakly positive implicative BCH-algebra. The weakly positive implicative BCH-algebras are characterized with the help of their self maps. Two open problems are posed