Abstract. Given a lattice $L$, the lattice, in fact the involution lattice, $\mathop{\rm Quord}(L)$ of quasiorders of $L$ is shown to be isomorphic with $\mathop{\rm Con}^2(L)$, the direct square of the congruence lattice of $L$. The isomorphism given is natural in category theoretic sense. As a corollary, a description of compatible partial orderings of a lattice is obtained.

AMS Subject Classification (1991): 06B99, 08A30

Keyword(s): quasiorder, compatible order, lattice, involution lattice, natural equivalence

Received August 22, 1994. (Registered under 5627/2009.)