A categorical view of varieties of ordered algebras
A categorical view of varieties of ordered algebras
It is well known that classical varieties of $\Sigma$-algebras correspond bijectively to finitary monads on $\mathsf{Set}$. We present an analogous result for varieties of ordered $\Sigma$-algebras, i.e., classes presented by inequations between $\Sigma$-terms. We prove that they correspond bijectively to strongly finitary monads on $\mathsf{Pos}$. That is, those finitary monads …