Functional Galois connections and a classification of symmetric conservative clones with a finite carrier

Abstract

We propose a classification of symmetric conservative clones with a finite carrier. For the study, we use the functional Galois connection (InvQ, PolQ), which is a natural modification of the connection (Inv, Pol) based on the preservation relation between functions f on a set A (of all finite arities) and sets of functions h ∈ A Q for an arbitrary set Q.