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