Tue, 29 Nov 2022, 1:25 pm MST
It is well-known that a function $f$ (of arity $n\geq 2$) preserves an equivalence or a quasiorder relation $\rho$ if (and only if) each unary polynomial function preserves $\rho$ which can be obtained from $f$ by substituting constants at all but one arguments. Thus the polymorphism clone Pol$\rho$ is completely determined by the endomorphism monoid End$\rho$. We ask which other relations and which monoids of unary mappings may have the same property. We introduce so-called generalized quasiorders which play a central role for answering these questions (moreover, they lead to new algebraic notions generalizing, e.g., affine completeness).
This is joint work with Danica Jakubíková-Studenovská (Košice, Slovakia) and Sándor Radeleczki (Miskolc, Hungary).
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