The aim of the talk is to study the notions of lax protomodular category [1] and \( \mathsf{Ord} \)-Mal'tsev category [2] in the context of (coherent) varieties of (pre)ordered algebras and to compare them, as has been done in the non-ordered context. We characterise varieties of ordered...

A variety is called Jónsson-Tarski if its algebraic theory contains a unique constant and a binary operation \( + \) satisfying \( x + 0 = 0 + x = x \).It is well known that this is equivalent to requiring the pair of morphisms \( \langle 1_X , 0\rangle\colon X \to X \times Y \) and \(...