  We represent finite join-semilattices and join-preserving morphisms as a
category whose objects and morphisms are binary relations. It is a quotient
category of $\mathsf{Rel}_f$'s arrow category, where self-duality arises by
taking the relational converse on both objects and morphisms. We investigate
the tensor product and the "tight" tensor product using both categories. We
also refine the categorical equivalence i.e. finite De Morgan algebras with
bounded lattice morphisms are equivalent to a category whose objects are the
symmetric relations.
