Coherence and compatibility: a stronger approach

TL;DR

This paper introduces more restrictive definitions of coherence and compatibility for multilinear mappings and polynomials, analyzing their theoretical properties and practical applicability through numerous examples.

Contribution

It proposes new, more restricted definitions of coherence and compatibility, and explores their implications both theoretically and practically.

Findings

New definitions are more restrictive than previous ones.

The definitions apply to a wide range of multilinear mappings and polynomials.

Examples demonstrate the practical relevance and limits of these definitions.

Abstract

In this work we present a definition for coherence and compatibility of multilinear mappings and homogenous polynomial classes. These definitions are more restricted than the ones proposed before. We began analyzing this new definition in a technical sense, searching for what it has in common with other approaches. Then, we moved on to a more practical analysis. Through numerous examples of different classes of multilinear mappings and homogenous polynomials we checked the limits on these proposed definitions and propose there is a vast field in which they apply.