  The set of all transformation monoids on a fixed set of infinite cardinality
\lambda, equipped with the order of inclusion, forms a complete algebraic
lattice Mon(\lambda) with 2^{\lambda} compact elements. We show that this
lattice is universal with respect to closed sublattices, i.e., the closed
sublattices of Mon(\lambda) are, up to isomorphism, precisely the complete
algebraic lattices with at most 2^{\lambda} compact elements.
