A categorical view of varieties of ordered algebras

Abstract It is well known that classical varieties of $\Sigma$ -algebras correspond bijectively to finitary monads on $\mathsf{Set}$ . We present an analogous result for ordered -algebras, is, categories algebras presented by inequations between -terms. prove they strongly $\mathsf{Pos}$ That those which preserve reflexive coinserters. deduce have a coinserter presentation, the coequalizer presentation due Kelly and Power. also show these are liftings Finally, equations proved extensions