Invertible invertible coproduct Coproduct morphism coproducts morphisms preorders Preorders antisymmetry antisymmetric preorder Preorder semilattice Semilattice semilattices Semilattices meet-semilattice meet-semilattices poset posets Posets Birkhoff's superset monoid monoid-like monoids monoidal monoid's Monoid Monoids isomorphism isomorphisms Isomorphisms Hasse Antisymmetry connexity linearly Heyting modus Modus ponens intuitionistic leit Z3 Z2 Z1 abelian Abelian non-abelian Dih3 composable forall codomain Euclidian subtypes Immanuel iff concatenative structs DeMorgan's getter OOP