Coarse classification of binary minimal clones

TL;DR

This paper classifies binary minimal clones into seven distinct categories, providing a comprehensive taxonomy that guarantees the preservation of clone types within each category.

Contribution

It introduces a detailed classification of binary minimal clones into seven categories, expanding understanding of their structural properties.

Findings

Seven categories of binary minimal clones identified

Each category's clone contains a minimal clone of the same type

Provides structural properties for each clone category

Abstract

We classify binary minimal clones into seven categories: affine algebras, rectangular bands, $p$-cyclic groupoids, spirals, non-Taylor partial semilattices, melds, and dispersive algebras. Each category has nice enough properties to guarantee that any clone of one of these types contains a minimal clone of the same type.