Artur Barkhudaryan, Charles University (Prague, Czech Republic)
Some universal properties of the category of clones
Our study was motivated by a problem of W. Taylor and O. C. Garcia about the breadth of the lattice of interpretability
types of varieties. It shows that there exist arbitrarily large rigid sets of clones (which give antichains in the above lattice).
Furthermore, every group can be represented as the monoid of endomorphisms of a clone. The question whether the
category of clones is algebraically universal is (as far as I know) still open.