On Mono- and Epimorphisms in Varieties of Ordered Algebras
Valdis Laan, Sohail Nasir · Communications in Algebra · 2015
We study morphisms in varieties of ordered universal algebras. We prove that (i) monomorphisms are precisely the injective homomorphisms and that (ii) every regular monomorphism is an order embedding, but the converse is not true in general. We also give a necessary and sufficient condition for a morphism to be a regular epimorphism. Finally, we discuss factorizations in such varieties.