Characterization of preclones by matrix collections

TL;DR

This paper characterizes preclones using matrix collections, describing their Galois closed classes through explicit closure conditions, thus advancing the algebraic understanding of these structures.

Contribution

It introduces a novel characterization of preclones via matrix collections and provides explicit closure conditions for their Galois closed classes.

Findings

Preclones are characterized by matrix collections.

Galois closed classes of matrix collections are explicitly described.

The paper advances algebraic understanding of preclones.

Abstract

Preclones are described as the closed classes of the Galois connection induced by a preservation relation between operations and matrix collections. The Galois closed classes of matrix collections are also described by explicit closure conditions.