Monomorphisms and epimorphisms in varieties of ordered algebras

An ordered algebra is a poset equipped with monotone operations. Homomorphisms of ordered algebras of the same type are mappings that preserve operatons and order. Varieties of ordered algebras are defined using inequalities (instead of identities) and these can be considered as categories. Our aim is to study different types of monomorphisms and epimorphisms (usual, regular, extremal) in such categories. We also discuss quotients, Homomorphism Theorem, freedom and factorization systems of ordered algebras.

The talk is based on joint work with Nasir Sohail.