An ordered algebra is called a sup-algebra if its underlying poset is a complete lattice and its operations are compatible with joins in each variable. In this article we study quotients and subalgebras of sup-algebras. We show that the congruence lattice of a sup-algebra is isomorphic to the lattice of its nuclei and dually isomorphic to the lattice of its meet-closed subalgebras. We also prove that the lattice of subalgebras of a sup-algebra is isomorphic to the lattice of its conuclei.
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