Functorial relationship between multirings and the various abstract theories of quadratic forms

TL;DR

This paper establishes explicit categorical equivalences between theories of quadratic forms and algebraic structures like multirings and multifields, offering new perspectives for future research.

Contribution

It introduces explicit equivalences and dualities between categories of quadratic form theories and algebraic structures, advancing the theoretical framework.

Findings

Categorical equivalences between quadratic form theories and multirings

Dual equivalences providing new insights into algebraic structures

Foundation for future research in abstract quadratic forms

Abstract

We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of quadratic forms in forthcoming papers.